You should be OK just re-combining them, but if you want to play safe you can find the queen in the bottom box (the old one) and remove her. No need for paper between them or anything, just pull the Snelgrove board.
I've used them for a couple years now with variable success. Had a few fail to make a queen in the top box, and have waited to late to remove the top colony for it to build up well as feeders on top of that huge stack isn't doable for me.
You will not weaken the bottom colony much if you open and close the doors on schedule (five days) while the top box is making a queen. Typically there will be several queen cells up there, so you can harvest some to replace less than stellar queens if you wish as well.
Note that under no circumstances should you EVER use a front entrance on the Snelgrove while there is any possibility of a queen going on a mating flight from the top box, if she goes into the bottom instead she will be promptly killed. Once she's laying it's less of an issue I think, but don't use a front entrance! That's why there are typically three, with the rear one used for queen mating.
Just to prevent swarms you and be pretty lakadasical about the doors and it will work fine, although not always. Bees do what the will not matter what beekeepers try to get them to do. Snelgrove boards do work very well if you find a lot of cells in a hive, just put them all above the board and make sure the old queen is in the bottom with only capped brood. The bees in the top box will tear down a lot of the cells (or you can use them for other hives) and it's unlikely the bottom will swarm with no nurse bees. Gotta move quick though.....