I agree with the comments and questions about the amp. You need to sort out any possible mains leakage from the amp before worrying about mystery oscillations in the pedal. Any issues with the mains connections can kill you. A typical pedal's 9V power battery can't.
And there's another issue. >>> IS <<< your pedal powered by a battery, or by an AC power adapter? If it's an AC powered 9V source, that could be leaking AC mains current too.
So do some detective work. It could save your life from electrocution. Get your voltmeter out, and set it to measure AC volts.
1. This one is first, as it presents the most danger to you. Is your AC mains socket properly grounded? Some are not wired correctly, and can make any plugged-in device be an electrocution hazard in some circumstances. The building itself could be your problem. You need to find a true earth ground and measure AC volts from the earth ground to the chassis and signal ground of your amp, and to all the metal knobs, jacks and switches of your amp. Anything more than 1-2 volts says that the amp can be leaking AC, or that the AC socket might be improperly wired.
This is not very likely, but it can happen, and it's so dangerous that you need to eliminate it first.
2. If you are powering the pedal from a battery, you can then proceed with tinkering caps and stuff. There's not enough power or voltage in a battery powered pedal to really hurt you. Yes, I'm aware of 9V battery powered shock devices on ebay and such, but those require some special setups to make the high voltage to make shocks. The pedal you describe is almost certain to not be able to produce a dangerous shock.
3. If you're powering the pedal from a plug-in AC to DC adapter, it could have the same shock issues as described in number 1 above for the amp. Do the same AC volts measurement on the pedal and a cable plugged only into the pedal, looking for AC volts between any metal you can touch to a known good earth point. A leaky AC to DC adapter plugged into AC mains voltage can kill you too.
4. Only after eliminating any possibility for the AC mains power to kill you continue messing with the circuit.