I agree with the above - as long as floor is not needing to be prized away from the box!
Hives adjacent, recipient prepared. Gently lift and swiftly move the box into position. Job done - come back the following day and look for bits of chewed paper near the hive entry. If none, then suspect the bees may need help in getting through.
I have, in the past, simply placed 2 x top screens on the recipient hive earlier in the day, to prevent any bees coming up from that hive, united in the evening and removed the screen the next day (or maybe two). Works well when a bit windy for fitting sheets of newspaper.
Best for weak colony on top, if practical, but chewing through paper (for a very weak colony) can sometimes just not happen. They may cluster in one top-most corner if no brood to service (BTDT).
I will add that if united three weeks ago, the colony would likely be strong enough, very shortly, to encourage a queen cell or two (demaree?)
Put the new queen in a 3-frame nuc or mini-nuc to start with - donāt split the colony to weaken the āgoingā part. That way you may well get a reduced crop of honey from it later in the season and have one (or maybe 2) other colonies which would be strong enough to over-winter or be united later.
Two new queens, if/when both get going, will provide more workers and provide you with a choice of which to keep if temperament of one is suspect. The other alternative later in the season could be to unite and buy in a queen. Choices, choices��.
RAB