Hi Bob,
Is your camper an aluminum sided camper or fiberglass?
If it is an aluminum sided camper, the ideal way to repair the rot damage is from the outside in. Meaning take the siding off, start and the bottom and work you way up.
When the siding is off, all the studs are exposed and you can repair them and then, staple the siding back into new good wood. I have done this many times. If you try and repair the camper from the inside only, and you have aluminum siding, there is no good way to restaple the siding to the stud.
For the wires, I would not do the splice unless you are forced to. Ideally you can unhook the ends and rethread it through the new holes. If that is not possible or practical then as was stated, gently cut the wood away to the hole and remove the wires from the old stud. Now how to get them back in. This somewhat depends on how many wires you have. How many are there in a bundle? Any pics?
IF it is 1 to say 4 wires of single strand 12 VDC wires, doing the grooving of the new stud and plating over is an option. If the bundle is large, like a coax cable plus 4 to 5 DC single strand wires, the notch might be too big as one big notch. In this case, try and create 2 smaller notches and plate over.
If the wire is 120 VAC romex cable, again ideally you can unthread it on one end. Drill a hole in the new stud and insert a piece of EMT conduit the width of the stud to protect the wire from staples, screws etc. then feed wire through.
Hope this helps
John