dabarrie OP: These may do the trick for you. I don’t know if your integrated amp has XLR or 1/4 outputs or not, but you can buy adapters or cables to go from RCA to XLR or 1/4". I hope these give you a good idea of what I had mentioned on my previous post. There are many other transmitters and receivers available and of course, they get more expensive as the quality, number of channels, features etc. improve but the specifications of these should suffice for what you are trying to accomplish. For best fidelity there is no substitute for wires though.
I hope this helps...