Tarheit makes good points.
It seems to depend on the colony (or the queen) if they accept her fast or slow.
The questions you may pose to yourself are:
"How many queens do I have to sacrifice?",
"How many hives do I have to support the queenless?"
If you have neither a supply of queens or only a few hives, I think a slower approach may work better.
Given that the queen was seen to be accepted, I agree with michael, the less handling and the less possibility to injury the queen the better.
There is always more than one way to skin a cat, that's of course if you're into eating cats.