I compete in Time Attack event here in Qc, Canada for the last 5 years.
I don't think it is more dangerous than HPDE but here no insurance company will cover you for time/competitive events.
I saw some people here using Hoosier A6. They go on the track, do 3 laps and come back into the paddock. Usually, their fastest time were in the 3 first lap so A6 kinda makes sense then.
I use PF01 pads for Time Attack. If you can use full slicks tires, get Michelin or Pirelli slicks and use them just for the time session. Run R-comp or streets tires during practice of those events
A full slicks will give you a good 2 sec a lap faster than a R6.