You do actually have an option here. The plastic mount under the headshell that is the contact point for the sled is only press fit into place (or, at worst, attached with a little bit of by-now dried out glue.)
You can solder a new set of wires to one of the ones left that's coming out of the bottom of the armtube, carefully pry up the plastic mount, and slowly snake the new wires up the post, through the arm, and then solder them to the plastic mount and press fit it back in place. No other disassembly needed.
The only thing to watch out for is a small copper tab that the ground wire is soldered to that is also press fit into a small channel with the plastic mount. You want to be really cognizant of that so you know how and where to put it when you reassemble it.
So in this case a new set of wires would have to number five: L+, L-, R+, R- and ground. I would recommend these as they are supposedly as limp and flexible as possible so they should snake up the tube easier than "regular" tone arm wire or even the same magnet wire Empire used:
https://www.kabusa.com/frameset.htm?/superflex.htm
As to how to connect them, the instructions for the 598 clearly show the arrangement of the wires as seen from the top of the sled, so it should be easy to wire the mount correctly. The only caveat here is to use an iron of the lowest possible wattage, use heat sinks, and be as sparing with the iron as possible as that plastic likes to melt really quickly. Soldering to the ground tab needs no such caveat as it's metal.
If the plastic mount is now loose in the shell after reassembly, a little dab of hot glue, or even Elmer's will keep it in place yet make it easy to pull out again if ever needed. (DON'T use an epoxy or any kind of superglue that would prevent another removal if needed. Heck, even a dab of mortite would be a good solution.) (
https://www.homedepot.com/p/Mortite-19-oz-x-90-ft-Grey-Weatherstrip-and-Caulking-Cord-B2/100152937)
It can be done...I've done it twice! (And used the mortite to keep it secure in place. It also has the advantage of acting as a bit of damping.)