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?
I am looking to do a jumbo-tron type of thing for a business picnic. All i would be putting it on is a t.v. I have a Sony handicam or a Canon Relbel EOS T3. Would either of these work to be able to stream live video wirelessly? Let me know please I need it for this Saturday. Also, if this wont work can you please give me links to the camera/materials i'll need to do it! Thanks!