EDIT: See Post 3 and Post 9. Don't use a wireless kit. A better solution is offered there, one that rethinks the original question instead of finding what the OP asked for.
End of EDIT.

Hilarious. I was just looking at this kind of product (on the internet) a couple of days ago. It was this: [Link: sewelldirect.com]

I've seen this kind of product work and work well, but it's been years. I expect you'll have to buy one and try it out to know if it'll work for you.

For other such products, search "remote control extender." There will be lots of responses. "Infrared extender" and "wireless IR Repeater" are other terms that will yield search responses for this kind of device.

It's a dumb device, so it will relay all commands that it sees. I don't expect that to be a problem, though.