Sounds like your wireless gizmo is a V/UHF FM tranmitter rather than a digital type, because with digital you might hear broken-up or “pixelated” audio but not hiss. Hiss in an FM system means there’s not enough signal strength from the transmitter to fully quiet the receiver, just like when you’re tuned to a distant FM station. Putting your hand on the strings probably acted to couple a bit more signal, thus the hiss went away. So I’d say you have found the problem and corrected it.
Yes... It had a little hiss while using a cord. But not nearly as bad as some I have seen on YouTube etc. And changing cords made it better or worse etc etc. But putting the wireless in made it completely dead quiet.