I used to stick Donny and Lola in the carrier while I did it, I kept them in a 4x2x2 hutch for 4 days after they came back from the rescue, then a 5ft space for 2 days, then 6ft for a day before giving them the run. When they were in the 5ft+ spaces I let them in the run for the 15 minutes it took.
Kerbie and Leo also went into their carrier, it never upset them, I gave them some pellets so they had something to do in there. They were a pain because we extended their space over 2 weeks before giving them the whole bedroom and picking up a rabbit everyday who had never been handled properly was always something to look forward to.. :lol: