Can I lay the bottle on its side with these stoppers?

If the fit is tight, test it before leaving the bottle on its side over night. I usually do not suggest laying it down because there are some bottles that are not perfectly round inside and although the stopper is in tight, I just wouldn’t trust it not to leak. If you need to lay it down to fit in the fridge, perhaps make a shorter stopper or one that fits down over the neck of the bottle. Example; stopper is 1/2″ above top of bottle.

The SS-9000 seals tight enough to be able to lay the bottle on its side when it seats tight.