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that happened at a friend's wedding, they moved them after dinner/cake/speeches. There really is no good way to do it, since those people are inconvenienced. In this case the tables were removed, not just moved, so those guests either had to find a table with an open spot, sit in an awkward chair along the wall or leave.
I'd have the venue staff handle it like they normally do although I'd try to see if there was a way to prevent having to do it in the first place bc it sucks for those at those tables