Can you move a hanging wasp nest without killing the wasps?

That's pretty hard. You would probably have to call a professional unless you don't mind getting stung a few times. Personally, I would go ahead and kill the wasps. That would be the safest method. You could hit the wasp nest down and capture it under a bucket or container (preferably clear so you can see if they wasps are dead or alive) in order for them to suffocate and eventually die under the bucket.