Can I change op-amp supply voltage without affecting circuit behaviour
The safest bet is to use the lowest common  rated voltage for target devices. i.e +/-12V

Full swing Slew rate, output current limit, cross-over-distortion and phase margin can be affected, so it depends what devices you choose. If you choose wisely, the supply variations ought to be insignificant from 12 to 18V as the internal functions are driven by regulated current sources.

Check for Zeners higher than the desired supply, many compensation caps will be found on old Op Amps that won't be needed on new Op Amps.