While I have a good large torque wrench at home, no way am I bringing that along in the trailer. I do carry a regular 1/2" ratchet, and often bring along my electronic torque adaptor, a combination much lighter and easier to store.
That said, I rarely carry either, other than the first trip after the tires get remounted, just as a check after a while. I very rarely find a lug nut has lessoned at all, let alone to a critical degree. I can pretty much tell with a wrench that I have adequate torque, if you are off by a good 10 ft lbs either way, the is no problem.
How many people actually check the torque on all your cars and trucks after wheel changes? They are no different than our trailer tires, and it is recommended to check torques on them to. Yet, many worry only about our trailers for some reason.