I doubt it'll break, but likely bend: the old one did, but I was never able to tighten it up beyond finger strength, because the cam in the QR end would slip. Tighter = less bend.
Additionally, with thread running the full length of the skewer, there's actually less structural material now: the skewer is, in essence, thinner. But as long as it's tight enough to prevent the wheel dropping out, I don't think it'll be a problem. I'm heading out again next week, so I'll let you know how things go in the field. I'm just thinking out loud here, but it might be an idea to add a bigger sized washer to the skewer end to give it a 'pad' to sit on against the frame, especially if it's welded or braised to the skewer end. This should lessen bending for the same amount of tightness, I should think.
Obviously the weight of the trailer is a factor here, too. I usually put most of the weight at the front of the trailer to prevent fishtailing down hills, but I might have to consider shifting the weight rearward if things get too bendy or breaky.