It should be possible in some way, but it does depend on the exact type of microphone capsule.
Can you disassemble one and post photos of the mic capsule and the part of the circuit board it connects to?
The only current Peavey dual mic system I can find is a PV-16, for which they do not give any info on the mics (other than how to turn them on or change the battery etc).
Most of the other mics Peavey sell are Dynamic ones. If that's the case with those, all you need to do is wire directly to the mic capsule. The two capsule connections go to the XLR signal pins & the case to the ground/screen pin.
If they use electret capsules, they need power so the battery would have to be retained or an external power feed used.
I've designed a mod board for upgrading a common type of cheap Chinese mics; you could use the same circuit to adapt an electret capsule to work with a standard XLR mic input that has phantom power, if that is the type of capsule they use.
The link to the circuit diagrams is just under the first two photos:
Robert Jenkins site & technology blog
You don't have to use the PCB, I've used the same core circuit built on stripboard for many years, before finally doing the PCB for it. You do not need the first transistor (JFET) for a common electret type capsule.
(The parts lists show detail parts are needed for each capsule type).