"Is there some way I can hookup the speakers without wires?"

You still need wire to the speakers. I think he (guessing) wants his receiver at one side of his room with his rear channel speaker outputs connected to a magic box of tricks that sends the info to three wall hanging speakers with no wires.

Larry has a solution but the cost of transmitters and a second receiver with enough channel inputs as you require and place to put/hide all this equipment at the back of the room (or hide it in the attic that you don’t want to go into!) maybe a little bit harder than just running wires.

Also your Receiver has Virtual 6.1 it has 5 speaker terminals the spec sheet on Sony’s web site says it has 1 pre out surround back (this is not very clear it may have pre outs for all three rear channels but it may just be rear centre) . Now because the surround processing will be done in the first receiver and you want to send that signal to another amp you may need two different transmitters .I am not sure that a receiver fed a two channel rear out put from one amp then set to 3 channel mode will work that well, yes it will look for the matrixed signals but on discrete 6.1 DVD discs will the rear centre go dead if fed just stereo signals? If you fed all the signals surround back via one type of transmitter and the rear surrounds via a speaker level transmitter to a second AV receiver with a multi channel in you would get exactly the right signals.

All you have to do now is set the levels correctly which I guess would take a bit longer than norm especially if you hide the second receiver in the attic! And you still need wires.

I really feel the best /cheapest solution is to go out a bit more get a different hobby! Only kidding no I think the best solution is to wire the suckers up now what wire to use……