Yeah.... I thought that was the direction I might be headed. Like I say... it is not real bad hiss, but not dead quiet either. The wiring all looks in tact, and maybe the guitar was always like that. I don’t know for certain. But I do know using the wireless rig eliminates the hiss/hum all together.
I have a Gibson SG bass guitar that I refurbished a few years back. It wound up with a distracting hum after I reassembled it. Drove me nuts. The wiring all looked intact as well. In the end, I redid ALL the solder joints and the hum disappeared. Sometimes, you just never know.
But, if your wireless rig does the trick, problem solved.