As the sub doesn't have a balanced input, you can use the existing wiring, but you will have to buy an unbalanced to balanced converter for the output of your receiver, and you will have to buy a balanced to unbalanced converter for the sub end.
That way, you're using the existing wiring as unscreened balanced cabling, which should work fine. If the in wall cabling runs along with the mains, there could be some hum, so hopefully, they won't have run them too close together.
You'll have to make up your own connecting cables from/to the converters.
S