@Redone , just to offer a little real world perspective on Warfarin;
The INR value of 2 means you will take twice as long to clot ( INR ~ 1 in an uncoagulated person )
if a person cuts their hand and takes 15 seconds to stop bleeding you will take around 30 seconds,
you do not bleed to death, your clotting just takes longer that is all.
I'm mechanical, very active and competitively race mountain bikes, i have had numerous crashes
on rocks and jumps over the years and i have never bled to death .
Best of luck with the surgery
Just to add , my driver on mechanical was also ( like you ) to have just the one OHS, both for myself and my family