Can an orc get Sting or Orcrist as a sacrifice gift?
No, you can never be gifted an artifact that hates your current race. Orcs can't receive Sting or Orcrist, and elves will never receive Grimtooth. (For this reason, an elf can always name Sting and Orcrist to be guaranteed Stormbringer as the first gift.)
Source reference: https://github.com/NetHack/NetHack/blob/NetHack-3.6.1_Release/src/artifact.c#L157