Hiccups, I'm finding out are normal. Especially if you get something stuck in the wraps. That would also account for the burning sensation.
My feeling is the wraps should be pretty strong to be able to last. You might make it sore, but as for damaging them, I think you would have to do something far more than hiccups, coughs, sneezes, etc.
The surgeons would have to expect that these are commonplace and would make things sturdy enough to be able to handle these everyday occurrences. Now, I wouldn't be doing situps or pullups at this point, there are limits, but...