You can also make a "humid hide" to put in when he looks ready to shed.
It's in essance a plastic container full of damp spagum moss, with a small opening for him to crawl through. He can crawl around in the damp moss which will help remove shed.
If you are worried about dropping him, then only handle him just above the floor(a few inches) or over a bed or table, so if you do accidentally drop him, he won't be injured.