Whereabouts are you located Nock? Do you have that kind of time? 3 to 4 weeks to get a laying queen and then another 3 weeks to start getting some new bees emerging. That is 6 weeks or more time lapse to the start of a recovering population. Again, do you have that kind of bee-time left for your region?
Personally at this time of the year, I would be crushing all cells etc right now, today. Put the nuc in with the nuc queen under a push-in cage with a bunch of her nuc bees for protection, and leave her under it for 3 days. Then I would go take the wife for dinner and a movie and such with no lingering concerns about the bees.