Just do a deep cycle battery.
Your converter system in the trailer is designed to have a battery. Without it, the only power capacity you have for the 12V stuff is from the charging circuit in the converter, which is essentially a trickle charger. You could also have somewhat inconsistent power from it, causing problems with things in the trailer. I heard of someone recently who started out with exactly what you propose. They couldn't figure out why they kept blowing light bulbs inside. Turns out they were getting too much electricity because ever since adding a battery, they haven't had a problem.
You have to remember, most of the systems in the trailer are designed for 12V. The exceptions are the A/C, microwave, and then the electric mode on your refrigerator, which require 120 from being plugged in. All the lights, radio if you have one, furnace blower/ignition, water pump, and probably a few things I'm forgetting all run off of 12V. They continue to run off 12V even at camp, and the converter simply keeps the battery charged as needed from you plugging the trailer in. Really, you could live at camp if you never plugged in and just charged the battery with a typical battery charger, it's just you wouldn't have those three 110 things.
Remember too, if you skip a battery, you can't run your refrigerator while on the road.
Running these trailers without a battery on short term basis (for loading it in the driveway, etc.) isn't a problem, I do it sometimes, but it should be kept at minimum.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR