Is it okay to buzz cut my hair on day 10 after FUE?

It is best to ask your surgeon about post operative care as each doctor has their unique regimen.   There is nothing wrong with cutting your hair in general.

All of the grafts are sealed in place after 6 days and the donor area will tolerate a buzz cut after a week.  If you have sterile instruments, you could buzz cut it immediately.  As soon as the skin is healed over and there is no open oozing, buzz cutting is fine.  Oozing usually ceases by the second or third day after your procedure.  

10 days should be fine to cut your hair. Some doctors say two weeks but at 10 days your grafts are pretty well established it'd take something pretty strong to really do damage to them.