I think you could well be right. If it were me, as a belt and braces approach, I would delete all cameras from that sync module, to be certain they are available for reuse and then I would delete the sync module. I would then add the new sync module and add each of the cameras back to the new one. Cameras may be released for reuse, just by deleting the sync module to which they are associated, but I wouldn’t want to chance that, otherwise, if they weren’t, you would have no way to access them to remove them, and that would result in a call to support, which might be a pain. Proof of purchase, blah blah, who knows what.
Not so easy if you have a bunch of them on the particular sync module, and they are up high, and you don’t have a record of the serial number, but that’s where having made a record of them would have come in handy. Hopefully there aren’t too many, and the OP does have a record, just to make life easier.
That’s what I’d do, in the absence of a specific routine to ‘swap’ a sync module, which I’ve never seen, and as you say Joel_Ek it doesn’t appear to be in the app.