Some thoughts......
Buy a decent size fiscus (1 you can use either in the cage or to take him outside for some sun or to park him in while you clean etc ) wash it to get rid of all the chemicals (do a search on that) and put him on that while you rearrange his cage. I do this for my boys while I do a thorough cleaning every 2 weeks or just to get them some sun when its warm. They look forward to this as a treat as the fiscus is bushy and they can hide or bask in the sun or jsut roam around in it.
What do you do when you clean his cage? Do you work around him? How big is this rearranging project? Are you getting him a bigger cage?
I am a believer that chams should not be overhandled....but I do believe that you should be able to handle them as stress free as possible for situations like this along with able to check them physically for any health issues, cage cleaning etc.
To do this I simply get them on a branch and slowly and carefully slide it under them until they grab on and lift them out gently and then onto the fiscus tree that is in a safe area and go about cleaning their cage. (with 1 eye on them all the time so they dont disappear & take off)
The great thing with a fiscus is that when they are in it you can move them anywhere you want. Mine have learnt that slow invasive branch = fiscus tree = adventure, sun and change of scenery and generally a fun time.
No matter what happens its good to be able to handle your cham occasionally for these types of reasons that way if anything major happens (vet visit, cage cleaning etc) he is not too stressed. Eventually he will have to come out of his cage so you may as well start training him now. Make it a great experience for him so that when it happens a few times he will learn that its ok and you are not out to hurt him...it may take a while but its worth it.
Good luck
