Is there a preferred time of day to do this?
There is an added complication. The transferred honeybees can't go back to the original hive which has to stay in place at least for 24 to 48hrs so the assumption is that the honeybees will have to be transferred into the new hive which will need to be sealed until the old hive can be removed.
I don't think this can be done easily during the day because returning honeybees will presumably want to head back to the original hive which needs to be kept out of bounds and open.
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I may be missing some of the subtlety of the situation, however …
Transfer the frames to the new hive in the afternoon and leave on the same spot until evening (or it starts raining hard). In the evening (or rain), after the foragers have returned to the hive, close up and remove (3 miles) and replace with your kill box for wasp action the following day.
Unless the bees are removed at least 3 (round number no-brain rule of thumb) miles away, some (variable number) of the bees will probably return to their old home position.
Bees shouldn't be left closed into their hive for any significant length of time in warm weather (you'd get away with an hour or so - not 48 hours).
Sounds like you are heading towards using (albeit temporarily) a third hive, to make a second transfer into, early the following morning, at the 'distant' apiary.... Moving the new hive even three miles without washing off the distress pheromone won't help because it will merely serve to attract wasps in the vicinity of the relocated hive.
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