Ignition switch wires

Yes, the wires can be spliced and soldered. You might want to check out this short video first:

https://youtu.be/4TjSYfLTHfg

First slide a piece of heat-shrink tubing onto one of the wires. Instead of twisting the wires together like we do with house wiring, I prefer to slide the two ends into each other, then press down any strands that may have stood up. Solder the splice, then slide the heat-shrink tubing over it to seal the joint. Use a needle nose pliers first to press down any strands so they don't poke through the tubing. Never use electrical tape to seal the splices as that will unravel into a gooey mess on a hot day.