It would be nice for us paint-by-number noobs if some expert would say EXACTLY what specs a capacitor should have, for this mod, like the type, voltage and tolerance.
Khron covered the tolerance question.
Regarding type, in general for audio path capacitors you want a dielectric which does not change capacitance with voltage or temperature, very stable. Film capacitors meet that requirement, but tend to be bulky. Of ceramic capacitors only C0G or NP0 dielectric meets that requirement (technically that is just a stability vs. temperature specification, but in practice ceramic dielectric formulations which are stable with temperature are also stable with voltage).
The biggest disadvantage of C0G capacitors is that only small values are available. In this application you need less than 1nF value, so C0G or film can satisfy the values needed.
Regarding voltage this design is phantom powered, so you know that the highest voltage any node in the mic will see is limited to less than 55V (48V plus worst case power supply tolerance), and most nodes downstream of the input pins will only see in the 35V range, so any cap rated 50V or more is fine.
Most film and C0G ceramic caps should meet that requirement as well.