While 4G. might be excessive it will certainly minimise voltage losses. Mzak, you don't state what amperage you are intending to run, but for this response, let's assume it is for normal camper uses. Unless you have really stepped up the TV electrical system you aren't going to be able to draw the rated current for long, if at all. The big wire electrical systems I've seen on automobile thump boxes always came with multiple batteries, extra alternators, and of course, deaf owners.
In which case all you need it a connector that is sufficient for the expected draw and a fuse to match. If that is the case, you could easily transition the 4G wire to a higher gauge number for the camper's normal connector or any other connector you prefered. Then transition back to the 4G wire on the other side if you wanted to. The voltage loss over the short distance should be negligible.
You wouldn't be planning a camper thump box would you?
If my assumption does not match your plan, please disregard.