If you are using drawn comb or frames with foundation I would give them a few days probably, enough to get the queen laying and larva hatching enough to lock them down after you move them. If you have other hives and can steal a frame of larva from them to give to the swarm, you could move it right away and then put the frame in with them to lock them down. Most of the time a swarm wont abandon brood.
Im a rookie so Im sure it has something to do with it but my swarm captured bees never play by the rules. If they are allowed to hang for a while in the box they seem to build really crazy comb which makes them (the waxed in flames or sideways comb) nearly impossible to easily extract. Im going to try to get on them faster then I did last year. I would say a few days should do it - you are dealing with bees who are looking for a home so I think they are more apt to stay in general.
I try to time it out so that the swarm traps are not out too long at a time. I do my homework and place them in areas that I had a concentration of swarm calls the year before. I do have a few that get hit a little by wax moths, but the bees make short work of them.
I have a large number of drawn frames for replacement if the moths do too much damage.
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