Sorry, I misunderstood your setup ininitally. So you use composite video cables, not component. And the issue is not a loose connection, but a dead TV speaker of two or even only one speaker built in to the TV.
If one of the speakers is dead, find somebody who fixes it for you. Usually it really is just a broken convention, and that's easy to fix with just a soldering iron.
In case there no way to do that, a Y-RCA-cable for adding the two stereo channel to one mono channel is just fine. One the one hand, this is recommended in many older console manuals (SNES, N64, etc.), on the other hand when I did TV repairs a decade ago, we also provided such cables for customers who wanted them.
I'm not saying there no better way to mix two sound channels into one, but I guess you wouldn't like to pay the price for a true electronic mixing device or have that bulk hardware set aside next to your TV.