When choosing to replace wheels also to use a 15" LT tire, a little bit of homework should sort out most of the issues. You do need to know how much your trailer weighs on the axles. Guessing, or going by the factory sticker is not a good way to do that. A trip to the scales is in order.
Here is just one example that might work. A Pirelli LT tire in 235/75-15 load range D would fit on a Sendel 15" 5 bolt wheel. Four of them would have a wheel limited load capacity of 8600 pounds. The tire capacity would be slightly higher than that. It might be typical to have a trailer that would have 3500 pound axles, so the real "limit" in that case would be the 7000 pounds of axle capacity.
There are other brands of tires and wheels that might also work, my point is to do a bit of homework ahead of time, and you likely can find a good fit.