Bobert, I was thinking overnight about your intention to use hairspray and thought I could make a useful comment.

I get the impression the asbestos is in an enclosed space. Hairspray is flammable and, dispersed as spray in an enclosed space may make the atmosphere vulnerable to any spark. So here's an alternative that's probably less risky but just as effective.

Your intention is to stabilise the surface of the asbestos for the lifetime of your occupancy and, hopefully, of the building.

Any physical disturbance to dry asbestos will cause dust to stir; this is to be avoided. The best avoidance method is to wet it; a bit of wetting agent (detergent?) allows the water to penetrate more than just the very outside.

Then you need to coat it. How does one coat asbestos that's wet?

Someone suggested PVA and that might be acceptable but so would water soluble plastic-based paint. The latter has the following advantages;
1 once dry it's more or less permanent (it won't dissolve under a drip like PVA),
2 it can be colour coded and/or painted over,
3 it can have appropriate labels/warnings painted over the background paint.

All the best.

Cheers, Rowan