Actually, you don't - you're just fine keeping the spring terminals and wire that fits them.
What you "should" do with the wires/cables, if you're going to use them nude/without connectors of any kind (yes, that's fine as well):
- strip the cable a bit
- twist/twirl the strands between your fingers, so the ends are not stray
- add a bit of tin
- strip a bit more of the cable, to expose fresh/unsoldered strands
- if the solder got sucked up, clip it so that only the tip remains tinned.
Don't twist the strands, keep them free/loose...this way they can arrange/align themselves, so that as much as possible of them touch/connect to the terminals. If you would insert a crude/tinned part, there may be just two contact points, in the worst case.
This is to ensure easier inserting and avoiding stray strands jumping across terminals.
Rest assured that hifi connectors (and wires) were mature technology in the eighties...and before that. Of course, they should be clean, not corroded or broken...exactly as the "modern" ones of today.
The guy...he just wants to fill his pockets - cable margins are made of wet dreams.