Here' what you need to know:
1) What opamp/chip is being used? If it's a straight JRC4558 it will be fine at 18v, but no more. Most similar dual opamps can run at 18v also (Burr Brown, TL072 etc...)
2) What voltages are your electrolytic caps rated for? Usually they'll up to 16v, around 50v or more. This will be clearly marked on the capacitor, both the capacitance value and the max voltage it can take. (Caps can be marked at the same value, but handle different voltages, EG: you could have two 3.3uf caps, one is a 16v, the other a 65v. This is what you need to know.)
3) Resistors and box/poly caps will be fine. Don't worry about these.
Post a gut shot if you can.