How about another suggestion...
Queen arrives. Inspect your colony and find your old queen, remove her and the frame she is on and place in nuc for safe keeping. Go through the frames and remove sealed, emerging brood and put these in a new hive in a new location. Leave eggs and open brood in the original location and share the stores frames between the two. Dummy down with wide follower boards/ make up frame deficit and return the Queen to her hive.
Your new hive, in a different location will be shedding flying bees as they make their way back 'home' so will be left with house bees who will realise by now that they are queenless so you can introduce your new queen, in her cage. I would leave the tab in place for a couple of days with a bought in queen, no point being cavalier only to get her killed. Judge their mood next time you visit, if they are over the cage, attempting to feed and you can move them aside fairly easily with your finger, snap the tab off and replace her. If they are all over it and difficult to move, give them more time.
If all is well (more than likely) and you remove the tab, the bees will be through the candy plug and have her out of there in no time. Allow a couple of days and have a look at the cage, you should see they've released her. Very carefully inspect the frames for evidence of laying or the queen, a fat, orange Buckfast should be easy to spot. Happy days, close up carefully and allow a couple of weeks before going through them again.
Meanwhile, having ordered another queen, kill your old queen. A week later return and break down emergency cells. When hopelessly queenless, introduce your new queen same as before.
Feed if necessary, to draw comb but don't overdo it.
Doing this early in the season and having been split, naughty bees or not, there will be less of them so easier on you and your nerves. Chances are you will get honey as well.
Good luck.