Deliberate Power Supply Sag
The power supply sag, while unintentional, has become part of the "sound" of an amp.  Indeed, more modern digital guitar amp simulators actually model that effect.  

But, for your question, this issue affects the main output power amp than op-amps.  

Op-amps have a specification, called PSRR, or Power Supply Rejection Ratio.  This gives you some indication on how much noise on the power rails will be coupled to the output of the opamp.  Normal opamps have a medium to high PSRR, while power amplifiers have a much smaller PSRR.

If I were you, I would first choose an op-amp with a high PSRR and just try it with your droopy rails.  Odds are high that you won't have an issue with just that.  But if you still have issues, then you will have to filter and/or regulate the droopy rail into something that works better.  

If this were my project I would put an LDO linear regulator to take the droopy 9v rail and bring it down to a nice and quiet 7.5v.  

A transformer and rectifier only helps if your 9 volt rail is AC and not DC.  You didn't specify which it is, but I am assuming DC because if it is AC then you are looking at the wrong thing.

Other than that, it is impossible to tell you what to do without seeing schematics for the amp that you have, plus schematics for what you want to add.