Dynos don't shag tyres. Bad operators that don't know where and how to set the bike up for a run damage tyres. Im glad to say that its a very rare thing these days.
If your tyre is within legal limits for the road then there is no reason why you shouldnt run it on the dyno.
I have run bikes at over 700 BHP with no major damage, the bigest problem is getting to much heat in the rubber and that tends to make the tyre look like its had a good track day.
I have seen tyres deflate on the dyno and also on top speed runs, think about how much centrifugal force is acting on the valve in your wheel. If you plan on doing high speed runs or have had a tyre go down for no reason then it may well be the valve, change it for one of the 90 degree ones.