With the battery out, you can have someone power up the trailer with shore power and measure the voltage at the battery terminals. If it is between about 12.5 and 13.5 volts, the converter is probably good enough to install a new battery.
Since your intent is to sell the trailer, you only want power so that you can show what is working and what is not to avoid the buyer's concern that nothing works and discounting the price to replace everything. Some of the older trailers relied on the battery to smooth out the power from the converters.
“You cannot reason someone out of a position they have not been reasoned into"
Al, K5TAN and Missy, N4RGO WBCCI 1322
2002 Classic 30 Slideout -S/OS #004
2013 Dodge 2500 Laramie 4x4 Megacab Cummins