His mini doesn't have J-wires, it has springs. My RAM Mini has springs. I don't know if any Mini had J-wires but I haven't seen as many as Mal
If the springs are deformed, they're toast. A dead or dying Polymoog is a good source of replacement springs. Handle with care, they deform easy.
Best way to clean them is a pipe cleaner dipped in denatured alcohol, brush the springs clean by twisting the pipe cleaner so the bristle get between the spring wires. Do not deform the springs.
I helped a friend with his Minimoog, turned out the former owner "cleaned" the spring contacts with automotive grease

Went through a lot of pipe cleaners on that one...
Dirty keycaps can be replaced, there are lots of home organs from the 70s that used Pratt-Read keyboards whose keycaps can be scavenged. I had a dead ARP Omni that sat in a basement and rusted beyond salvaging, but the keycaps were clean. I gave the whole thing to a tech for parts.
WD40 is a water based lubricant, it is not a cleaner.