SWA doesn't have an escort fee, because they don't have an escort program, as such. Unaccompanied kids are given a neck-pouch ID, preboarded first, and seated in the bulkhead row if there is space, but that's pretty much the extent of the "service". They do carefully check the ID of the person claiming the child at the destination gate, though.
I'd say that as long as he's an experienced flyer and not frightened to do it, AND as long as he doesn't have to change planes, he should be OK. You can ask for an escort pass to take him to the gate and stay there until the flight departs, and his dad should meet him at the gate at his destination. You should also give him some pocket money, a phone card and all relevant numbers, and a packed lunch which is NOT pbj (in case there is an allergy alert on the flight), plus some quiet things with which to entertain himself.
The only possibility I see for a gotcha is if the plane hits a weather delay at the city where it stops, and they allow the continuing passengers to deplane. I don't know how SWA handles minors in a situation like that -- you should call and ask.