I'd suggest not going without a battery. A battery will act to smooth out spikes in DC electrical loads. Sharp, sudden spikes in load on a power converter will put a strain on it and will be sure to shorten its life. Turning lights on & off won't be much of a strain. But slide outs, electric stab jacks or a electric tongue jack are a different matter.
Also, campgrounds are typically in VERY rural areas. Rural areas are prone to power outages after summer storms. Without a battery and without AC power, you will have no electrical power at all. Without any power either AC or DC, your refrigerator will not run and your beer will not be cold. Even when running on propane, most RV fridges need some source of 12v electrical to function.
For your needs, even a smaller group 24 should work. A group 24 battery and a box can be obtained for a lot less than what a new power converter would run.
FAA A&P mechanic, ex-RV dealer parts dept
Retired B-52 Gunner/Flight Examiner, B-52 Crew Chief
2016 Jayco Eagle HT 29.5 FBDS w/ 15,000 BTU AC, 50 amp service, upgraded counter top, thermal pane windows, elec. stab jacks, outside grill, backup camera and MORryde pin box.
2011 GMC 2500HD DURAMAX/ ALLISON