I'm sure that if you wanted to handle in shed you could, but I personally wouldn't because they tend to stress out a little more when they're shedding cause they have limited vision, etc.
I never have a problem with feeding during shed though, but I only feed F/T. I don't recommend feeding live while an animal is in shed for the same reason that I don't handle in shed. If you feed frozen/thawed or pre-killed then the animal will either take it or not, depending on how they feel.
I never heard that they have extra sensitive skin after a shed, I handled mine right after I had to soak him and help him get his shed off, and there was no problem.