That's much easier if they're already separated
I would put them straight into the new cages you have, without the fluff and give them 2 or3 days to settle in and build a nest out of the paper, and no cleaning or moving things around for a couple of weeks till they;re fully settled. Yes they'll be having a change but best they go straight into the new cages you have - they will settle better than having another change later.
Is one bigger than the other? If so how about David and Goliath? A theme is a good idea - films, books, comics.
I went through loads of lists online when choosing ours and made a shortlist but ultimately it ends up being my Stepson's choice (although I slightly over-ruled on the last choice!)