Normally, you'd do an "update Request" to suggest moving a listing from one category to another. That will entail a re-review; the site remains listed until the re-review.
What can happen then?
(1) The site may be removed altogether (this is not highly likely); the editor having concluded that it shouldn't ever have been listed.
(2) The site may be left alone (this is the most likely); the editor having concluded that the other editor knew the ODP taxonomy and you didn't;
(3) The site might be listed in both places (very unlikely unless one was a Topical and the other a Regional category)
(4) The site might be moved and a new listing appear immediately; the editor having concluded that a good case could be made for the move (not particularly likely but possible
(5) The site might be moved to the other category for later review (this should be very rare, but I have seen it happen)
Remember that the decision will be made based on the needs of the ODP and the surfer: your desire will not be a factor at all. But ... if the editor made a mistake, we do want to know about it, and I'd not penalize one plausible request for a category move (even if I rejected it.)
I would, however, very strongly suggest NOT making more than one such request. Chances are, as I mentioned, that the mistake will be in your understanding of the taxonomy, not in one of the other options.