I do not know if a sharp knife hurts less but the cuts heal faster (in my experience anyway) than blunt knife cuts.
My last major self inflicted cut (stabbed my left palm while trying to drop the point of my knife on a hand held stone - work finished off by Dave Budd on his grinder
)
The 3/4" long cut was actually a stab and the point stuck enough to need pulling out. I did a "wriggle" test and everything worked despite my being able to see the white bits inside the cut when I inspected it visually. I simply bound my fist up around a wound dressing and when I inspected it 3 days later it was neatly healed with no sign of infection. No real pain when it happened, none during healing and no lasting ill effects - except a visual scar in my palm. The worst of it was the annoyance of not being able to use my left hand for 3 days while it was bound up....
My most painful cut was a gouge from a tree branch that ripped a ragged but shallow 2" cut across the inside of my left forearm - stung like a pig and took over a week to fully heal and has left a more visible scar than the knife wound!