Aw, I'm so sorry about your duck! Though I think you are definitely right, if I recall correctly they can't fly (breed to be heavy set) as they are meat ducks, so this is definitely something that can't be long term (as he can't fly away from predators). My Orpington Duck is definitely a chunky boy!
Ok, this may be an extreme suggestion, but this worked for a bunch of chickens we had. So my Grandparents have a big property, and we kept some chickens out there. We let them free range and such while my Grandma watched from the porch, but one time some hawks attacked (and my Grandma didn't see them). All the chickens scattered, and it took the rest of the day to get them. Now, with all the coyotes, hawks, and raccoons that my Grandparents property had they would not have survived the night, so we were getting desperate as the sun started to set (there is never a night there isn't a coyote howling). So, we were all just pitching ideas like crazy because even if we did decide to let them stay in the woods overnight, we didn't have high hopes they would survive (our rooster had small spurs) the night. Do you have a cast net? What we did was we all surrounded the chickens and then my brother threw a cast nest over the birds and we quickly jumped and stilled the poor chickens. The reason why I hesitantly suggest it is because of the fact that they could get injured as they try to flap their wings and escape, but from your situation, it sounds like the duck may die if you just leave it there (especially if it's starving, alone, and in the cold). Our chickens didn't get hurt during the process though, but we changed the coop so that it had an enclosed run so we didn't repeat the experience again. But with the way you describe your duck, I think that any injury could be treated so it might be worth it. When all else fails I guess. I am by no means an expert, just a duck lover though! Just a suggestion, and even if this doesn't help, I really hope you get your duckie back <3