Has anyone ever had this happen?

I am replacing an axle bearing at work and I set it off to the side for when I had some free time.
A co-worker decided to help me out and took it to his work area.He was using a cut-off wheel to grind the collar,so that the bearing could come off.
He accidentally ground too deep and now there is a nick in the axle about 1/16 deep and about 3/8"
long.
This is a stock axle behind a warmed 383 4-speed,with a 4:10 gear.I drive it pretty hard and it will see limited track time.
Would you press a new bearing and seal on it and forget about it? I'm sure this is not the first time it's happened to someone grinding the collar,I don't know if it severely weakens that area or not.