I feel that any sort of cable that locks the bike and the trailer together through at least one wheel so that the whole thing won't roll, and you'll put off most passing opportunists - the two bits can't the separated, it can't be ridden away, even picking it up and putting it in a van is going to be more hassle with it all flopping around, plus the extra length.
Given that weight is less of an issue, I'd have a u-lock through the frame/rear triangle of the bike, another U-lock through trailer wheel and load bed as you suggested, and then a reasonably long cable with a loop at each end to join the 2 together, and maybe also go around your chosen immovable object. Save carrying the bike in, too.
Or, put the folded bike in the trailer and wheel the whole thing in like a trolley!