I've looked at a number of designs for pA meters. There's more issues than just ripple, you want to avoid noise coming from all sources. Batteries can be contained within a shielded enclosure, once you go to mains operation, you note need to filter the noise coming in through your power supply and deal with capacitive (or direct) coupling via the power supply.
Most pA meters don't require lots of power, and an alternative option is to use several small lipo cells in series. The charger for these will likely be noisy (as well as introducing coupling issues) so don't use it when you're charging.
There's a very simple pA meter
design that runs from a 9v battery and has a resolution down to 100's of fA. Have you seen that?