Summarised_solution:
General purpose high current, high gain SOT23 bipolar & MOSFET transistors are available at modest cost. These will work if the part is used as an on/off saturated switch and will probably work in other roles.
Required polarity can be determined by a single measurement.
SOT23 small signal transistor is usually -
b c e for bipolar
g d s for MOSFET
as per diagram below.

Measure voltage 2 to 3.
If 2 is +ve wrt 3 then = npn or n channel.
If reversed then pnp or p channel.
A high current high beta npn or pnp will work in most bipolar cases.
BC817-30 / BC807-40 are good.
-40 means AVERAG current gan of 400. ie 250-600 range.
50V, 800 mA rated for thisFairchild example sold by Digikey
Rbase of 1k to 10k should be OK.
MOSFET N Channel needs low Vgsth.
CES2310 utterly superb if you can get them.
OR
36 cents /1 in stok at Digikey for this
2.6v Vgsth , 60V, 1.A continuous
IRLML2060
But, Better! -->
INFINEON BSS205 N !!!
20v, 2.5A, < 100 mohm Rdson at 2.5V Vgs.
In stock Digikey 37 CENTS /1
No gate resistor needed. Use say 1K if desired.
For P Channel use Digikey selector guide to select out specs of chouce then sort by price ascending in quantity 1.
This is a truly marvellous part for amateur general use.
Be ware of 20V Vds max but otherwise marvellous.
eg 0.2V Vds at 1.5A at 2V Vgs.
500 mW disispation and 250 K/W mean due care needed thermally (as in all SOT23)
BUT very low Rdson will keep it OK in many cases.
eg 98% of these have < 80 milliohm Rdson at high temperature.
At say 1A dissipation <= 80 mW for 20 C case rise on modest copper.
If you MUST have 30V there is the very nice 41cents/1
IRLML6346
Best Answer
The transistor isn't critical.
A \$25\:\text{W}\$ output into \$8\:\Omega\$ means a peak \$Q_{415}\$ emitter current of \$\frac{20\:\text{V}}{8\:\Omega}=2.5\:\text{A}\$. (Resistive load assumption, which isn't entirely accurate.) \$Q_{411}\$ only has to supply its peak base current. \$Q_{415}\$ minimum \$h_\text{FE}=50\$. So this means \$50\:\text{mA}\$, worst case. Although I do not like this design, the maximum current pulled through the \$V_\text{BE}\$-multiplier by \$R_{447}\$ and \$R_{449}\$ is \$19.5\:\text{mA}\$. (Or should be so long as the \$25\:\text{W}\$ is respected.) That means a maximum drop across \$R_{437}=68\:\Omega\$ of \$\approx 1.33\:\text{V}\$ due to the \$V_\text{BE}\$-multiplier. But as the rail is \$+38\:\text{V}\$ (with ripple? haven't checked that) and a peak base drive voltage to \$Q_{407}\$ of \$\le 23\:\text{V}\$, there's \$15\:\text{V}-1.33\:\text{V}\$ or \$\ge 13\:\text{V}\$ of available headroom for \$R_{437}\$ needed voltage drop to supply \$Q_{411}\$'s base. Enough that you could easily saturate \$Q_{411}\$ and not have to worry about it. So there's really no need for high values of \$h_\text{FE}\$ for \$Q_{411}\$. I'm sure anything better than a minimum of 50 would be fine. It must also squeak by standing off at least \$33\:\text{V}-\left(-20\:\text{V}+2\:\text{V}\right)\$ or \$V_\text{CBO}\ge 51\:\text{V}\$. That said, the 2SD699 is rated for \$V_\text{CBO}=180\:\text{V}\$. So, you may be able to get by with anything rated \$V_\text{CBO}\ge 80\:\text{V}\$. Maybe a little less if you are stuck looking around, though of course you'd probably prefer something rated as high as what they already used. But at least you have an idea about what you might be able to get by with, if you need to.
In short, you want the same package (TO-126 or TO-225AA or equiv) and you want it to be an NPN. Since the peak collector current shouldn't be more than about \$50\:\text{mA}\$, I'd double that for a cushion at \$100\:\text{mA}\$ which is... pretty much any BJT at all. So that's not going to be an issue and you can just not worry about it, for now. I'd probably make sure that \$80\:\text{V} \le V_\text{CBO}\le 200\:\text{V}\$. With larger values being preferred while realizing that lower values may be acceptable and work well. A lot of BJTs may fall under your need here, so this is one parameter to keep in mind as you look.
I'd assume that the worst-case dissipation requirements are going to be met so long as you select a similar package. But the worst case instantaneous dissipation will be about half-way through its active part of the half-cycle. That dissipation value is so small that I'm not at all worried. The package is over-kill.
Notes
If you are interested, I'll sketch out some detail about my thinking process. This exposes any errors I may have made (which may hurt how others see me should I care about that) but it also may teach (should I be lucky enough to have avoided making serious errors.)
This site is more about electronic design as I see it and less about giving simplistic answers. (More about learning to fish than about being given a fish.)
That said, here are my thoughts in the order in which I had them:
That's about where I stopped.
One does need to just understand the basics of a typical class-AB output stage and then just go around the loop, so to speak. You do need to think about one entire cycle of AC over its maximum output range. But that way you can list out the important details as they arise and then also know what details are likely less of a worry.
One last point I need to add. This schematic drawing was obviously arranged so as to minimize wasted white-space and reduce the number of pages required. Hardly a nook or cranny was missed. It's not the worst I've seen by any stretch. One can easily see the basic skeleton of a decent schematic in there. But it's as if they've tightly packed it into a box with many bones akimbo. If I wanted to fully replicate this design and verify everything I see there, or should I be interested in finding design errors, I would completely and totally re-lay out this schematic so that it was more readable.
The schematic drawing is really pretty bad, as shown. Those two pull-down resistors, \$R_{447}\$ and \$R_{449}\$, look almost as though there is some mysterious signal coming in through \$C_{427}\$ via them into the output section. Signal is usually arranged to flow from left to right. So that's what I tend to expect when I see things laid out like that. But it's really just a pull-down with \$C_{427}\$ helping to sustain a more constant current in \$R_{447}\$ over a cycle. In fact, that capacitor detail (kind of a bootstrap concept) was almost certainly included because of the above comments I made about the negative-half-cycle. If they'd have missed including it, then I'd have stayed more leery of this schematic. But it was there, so I felt better.
(If interested, just walk your mind around this loop: start at the (+) end of \$C_{427}\$ (the output), then through the BE junction of \$Q_{417}\$, then through the BE junction of \$Q_{413}\$, which takes you to one side of \$R_{447}\$. The other side of \$R_{447}\$ is the (-) end of \$C_{427}\$. So if \$C_{427}\$ maintains its voltage for a moment then the current in \$R_{447}\$ is also maintained. Which is a constant current, therefore. So \$C_{427}\$ helps sustain a constant current in \$R_{447}\$ which compensates for all the movement going on with the output. This is why \$C_{427}\$ is an important addition to the circuit. It has nothing at all to do with signal.)
I always recommend at least considering the idea of re-drawing schematics before attempting to spend any significant time studying them. There's usually plenty of room for improvement. See here for more thought about this aspect and some guidelines.