Gluing small parts with hairspray?
AFAIK those "bead glues" work on a completely different principle where the sheen on the individual beads is a water-activated glue and so the finished piece needs to be sprayed with just clean water to adhere the beads together.

There are a number of "weak glues" known which could be worth a try:


thick sugar syrup (naturally water soluble, thus removable)
a mixture of baking flour and water (similarly water soluble)
from this answer comes a recommendation for the "Spray and Play" glue, which can be found for sale online but whose website has since gone rogue. Probably due to the negative feedback received on Amazon.


Of course, for any of the above I'd recommend trying with a few pairs of expendable bricks, whose total cost might be lower than any one of your prized collectibles.

Another avenue would be to increase the clutch power to prevent the separation of the pieces. For example you could place thin pieces of paper, saran wrap or tinfoil between the LEGO pieces that need to be held together. The additional material will prevent the pieces from returning to their original shapes, this tension will make accidental separation harder. And if you get the size of the insert small enough and the placement precise enough, nothing will stick out from between the bricks and so the insert will not degrade the display value.