I'm glad you're being sensible about this LR.
Blue asbestos (crocidolite) is far more dangerous than white (chrysotile) but both can be dangerous, causing asbestosis or mesothelioma. However I doubt your exposure to either was sufficient to cause any problem. Symptoms occur twenty to thirty years after exposure, you say you were a child when your dad was cutting it up & have had none. Plenty of people had same exposure and even ironing board covers (if damaged) released asbestos fibres, never mind things that went behind cookers& the like. I've probably had some exposure myself.
Got this from NHS site:- "..you would need prolonged exposure to asbestos fibres, usually over many years, before you develop asbestosis."
I expect you've had a chest x-ray at some stage over the years which was clear.
Forget it. If you develop an asbestos related disease when you're eighty-five which is unlikely, you won't care too much. However it is extremely unlikely so don't be spooked.