I have successfully fostered - several times - onto ewes who'd lambed a week earlier, so don't get too stressed about getting a lamb today or tomorrow, although that is of course preferable. Some of the ewes had been milked for colostrum for the freezer, but others hadn't been milked, and I can only think of one or two that didn't have milk for the foster lamb. Up to three or four days I wouldn't expect a problem - and I've done one where the ewe had lambed 10 days previously!
Experienced girls who have lost their own lambs will generally take a foster lamb whether or not it smells of their own lamb; they are just desperate to have a lamb to love. So if the dead lamb gets a bit stinky I wouldn't be too worried about saving its skin to use. Again, it helps, but don't get too worried about it.
It's often the first lamber or two that give the problems, isn't it.
Sometimes I've felt that we were going to have the most disastrous lambing in history, but generally after a few false starts and hiccoughs, things start to flow as they should.