I have been an R.N in the operating rooms for 20 years now. Here is what I would do.
Make sure the therapeutic level of the anticoagulants is correct.
Make sure your doc says your fit.
But you need to wear all the gear.
If you do happen to have a major off and a sudden decelerative injury tears your aorta your as good as dead whether you were on anticoagulants or not.
However (always a however) certain seemingly minor impacts to the head, even with a helmet, may cause bleeding subdurally. So if you wack your head a good one get medical follow-up. A bleed like that can take days to kill you so even if you feel fine go see a doc.