(Terminology nitpick: you have 2 speaker cables and 4 speaker wires. A wire is a piece of metal; a cable is a bundle of wires.)

I'd suggest installing an RCA connector insert for the subwoofer, and a common “ethernet” modular jack insert (8P8C) for the speakers. That gets you 8 pins, twice as many as you need, which you can then double up to improve the conductivity (probably would be fine without, but we might as well).

Of course, this means you're going to need an adapter to go to your speakers, since modular plugs aren't designed to have custom wiring inside the plug. Something like this (not a recommendation; just search for "rj45 breakout" and find lots of options) will do the trick (or you can get ones with a socket to run a cable to, if you need to avoid a bulky object sticking out of the floor box).

On the inside of the floor box, you can make splices from speaker cable to 2 smaller wires suitable for a punchdown ethernet jack, or run regular Cat5 cable to the other end.

I'd also stick a label on the plate to clarify it's not an ethernet socket.

(Don't worry too much about using thin wires — the shorter the length, the less it matters.)