Ripping off old plaster

I wouldn't say there would be if it is in the 30's probably just horse hair, I've just taken a 1930's back to bare brick and dropped all ceilings.hopefully nothing comes back!

An easier and cleaner way would be to go over the existing with plasterboard then skim

If there are strands in the plaster then it is more likely than anything else to be horse hair or the like. It was used to help reduce cracking as the plaster dried. If there is asbestos in your plaster, then so long as you don't suck it, lick it, grind it up and snort it, eat it or otherwise do anything particularly daft you are perfectly OK! If it turns out to be the grey stuff it is not overly scary and with sensible precautions you can remove it yourself and take it to the local tip. Just ring them up first and they will instruct you on how they want it done. If it turns out to be the blue stuff then you will need specialist contractors in to remove it as that is more dangerous. Until you get your results, don't panic and don't eat any!

Alot of the old artex is asbestos. If in doubt get it tested it's not too expensive.

If in doubt of asbestos, whether it's walls or ceilings, for reassurance I find boarding over the area the safest.