The writeup you linked to doesn't say much useful, but it appears these are bare speaker-type headphones (guessing from the size and shape). That means they are probably small speakers with 4 or 8 Ohms impedance.
You don't want to put a pot in line with speakers. That wastes power, doesn't present the right load to the amplifier, and probably messes up the frequency response due to the impedance change. The best place to put a volume control is in the signal path, not the power path. This means put it at the input of the amplifier that drives the headphones.
Whatever is driving the amplifier input is probably a "line" output. These usually have a few 100 Ohms impedance with a nominal 1V signal. A 1 kΩ logarithmic taper pot would be about right. Nowadays logarithmic tapers are harder to find because old fashioned analog pot volume controls aren't used that much. Nowadays the signal is handled digitally somewhere anyway, so the volume control is done by a digital multiply. If you can't find a logarithmic taper pot, it's not that big a deal. A linear taper will have a lot of change at the low volume end and not much at the high volume end, but for just setting a comfortable headphone volume it's probably good enough.
You can make a linear pot non-linear by putting another resistor accross the output. This doesn't make it logarithmic, but should spread the volume range out a little. Personally I wouldn't bother with this unless you've tried it directly and really didn't like the result.
As for avoiding hum and noise in audio, make sure everything is shielded. If necessary, mount the pot in a small metal box with the box grounded to the bottom lead of the pot, which should also be the ground for the input and output cables.
The slot is for adjustment with a flat-headed screwdriver (instead of a knob), and is not generally intended as a feature for the knob to engage with. Just use the same type of knob that you'd use with a purely cylindrical shaft - a knob with a setscrew:
Best Answer
What's your rationale for not wanting to solder to the terminals of the pot in Fig.1 ?
They are designed to be soldered to wires. The best practice is to hook the wire through the little hole, and then solder it. (Special MIL-spec bonus if you can prevent solder from wicking up into the stranded wire.) For strain relief, add heat shrink such that it covers the terminal and some length of wire.
Update. In response to Blake's comment.
I can give you a couple of tips on soldering.
Solder should melt on the pin (that included wires) rather than on the soldering iron. That means that the pin should to be heated up sufficiently.
Flux helps remove oxidation. If you use no-clean flux, you don't need to clean it.
Leaded solder has a lower melting temperature, so it's easier to use than lead-free.
May be, I'll be able to find a good tutorial video and post a link in another comment. Also, there ought to be a good "soldering tutorial" thread or wiki on this board too.