Posting a self-answer to tell you how I fared.
(Yes, it was a year ago... Took me a while to get around to this. Life got in the way.)
I had 8 old model-kits to put together. 4 of those were still unopened with the contents, including the water-slide decal sheet(s), sealed in plastic bags.
2 of these models were identical WW 1 era bi-planes. I think Mike originally intended to use these as part of a diorama showing a dogfight between these 2 British planes and a German plane (the Red Baron) that he already had completed.
Attempt 1
So knowing I had a spare for use in attempt 2 in case it would go horribly wrong, I used the decals of one of these planes as a test-case.
No luck: They failed to separate from the backing even after a very long soak in warm water.
So the sealed bags hadn't been enough to prevent degradation. Since all model-kits were roughly the same age and by the same manufacturer it didn't make any sense to try the others. Trying the decals that hadn't been bagged made even less sense.
Attempt 2
So I bought a pack of blank decal-paper for use in a laserjet printer. Put each original decal sheet on a flat-bed scanner and made a 600 DPI scan. Then printed each scan on the blank decal paper using the color laser-printer at the office.
Did a test-run on plain paper first to make sure the resulting print was exactly the right size and to verify how the colors came out.
I found I had to saturate the colors a little extra to compensate for the laser-printers slightly washed out colors.
After printing the first decal on the transparent decal paper I checked colors again and I found I needed to add even more saturation to get the colors just right.
Then I printed all the decals and I had a fresh set.
Conclusion
Copying the decals onto fresh paper turned out to be a very easy and cheap (€3,- for 10 sheets of A4) solution and I will certainly be doing this again when dealing with old decals.
If you are not certain about any decals that have been lying around for a long time it is certainly worth the effort to make a scan of them "just in case" you need replacements. Trying to scan them AFTER trying to use them won't go too well.
I had a flatbed scanner at my disposal, but you can probably get away with a smartphone photo of the decal. You just need to use some image-editing software to stretch the photo into a rectangle if you took the photo at an angle.
PS.
Blank decal paper is available for inktjet printers too. You will have to bear in mind that most inktjet inks are to a certain extend water soluble when they are not 100% dry. And it takes a very, very long time to really dry.
(I had inkjet prints blot when they got a few drops of water 6 months after being printed.)
Unless you are absolutely certain your inkjet ink will not smear when come in contact with water, using an inkjet to print your own water-slide decals doesn't seem a very good idea.