Fastest, most efficient: Hire a company with the equipment to do the job. We don't know where you are so providing links is challenging.
You did not tell us which "Sony Handycam".
Titan makes good wireless video gear, assuming the camcorder has the right connectivity. Use of a dSLR is not a good idea. Overheating (documented in the manual) will cause the camera to shut down until cool enough to start using again.
bhphotovideo has the wireless video gear... camcorder attaches to video transmitter; video transmitted to base station. Base station connects to monitor.
We also don't know which TV, so no way to know if it has appropriate connectivity.
What about audio?