Basis turntables makes one line of cables that are very, very good.
Of course it's possible... Even if the wires are soldered inside the chassis, you should be able to open it up and replace them.
From your description, the stock cables are basic mini-coax type, which is very common with vintage equipment from Japan. You can improve the sound, but how much depends on the rest of your system, not only the cartridge and phono stage.
Whatever you pick, make sure it is shielded correctly. Signal levels from a cartridge are very low, so shielding is mandatory. Even if it won't hum now, it's just a matter of "when", not "if".
Also check the recommended loading of your cartridge. In some cases, the cable's capacitance could influence the sound quite a bit.