Electronic – How to know whether a potentiometer is a linear potentiometer or audio potentiometer

You say this is a low volume product. Therefore, just do one last lifetime buy. Even if you could find a drop in replacement, that would likely go obsolete soon too for the same reason. Doing a single lifetime buy will likely be cheaper than the engineering effort to find and then deal with parts that are not quite the same.

All a volume control is, is a variable voltage divider.

You don't have to have it as a smooth track - you can do it with switches and fixed resistors.

For instance, the following circuit:

^{simulate this circuit – Schematic created using CircuitLab}

With no switches closed, Vout == Vin.

With SW1 closed you get \$V_{OUT} = \frac{R2}{R1 + R2}×V_{IN} = \frac{100k}{10k+100k} = 0.9×V_{IN}.\$.

With SW2 closed you get \$V_{OUT} = \frac{R2}{R1 + R2}×V_{IN} = \frac{10k}{10k+10k} = 0.5×V_{IN}.\$.

With SW3 closed you get \$V_{OUT} = \frac{R2}{R1 + R2}×V_{IN} = \frac{1k}{10k+1k} = 0.09×V_{IN}.\$.

You can also combine switches. With SW1 and SW2 closed the "lower" resistor becomes \$\frac{R2×R3}{R2+R3} = \frac{100k × 10k}{100k + 10k} = 9090\Omega\$ so the output voltage would be \$\frac{9090}{9090 + 10000} = 0.476×V_{IN}\$

You can have as many switches as you like, and whatever combination of resistors suits your needs.