If you'd seen my efforts at soldering, you wouldn't be asking me for advice 😉
Removing the wires should be a case of pulling gently on them while applying the iron to the solder pad - as soon as the solder melts, they should come free. If they're not loose after a couple of seconds, remove the iron to avoid overheating, and re-think. You may need more power or a larger tip.
Remove one wire at a time if possible - you'll want to cut the cable tie bundling the P wires to the MM wires, and it may be easier if you can separate the black and white wires a few inches along their length.
https://mightyohm.com/blog/2011/04/soldering-is-easy-comic-book/
https://www.premierguitar.com/diy/guitar-bass-mods/guitar-soldering?page=1
Personally I'd go for the terminal block, as it's hard to get wrong - but best of luck either way!