I'm having kidney stone removal surgery at the end of april via the uretha. Can I get a tattoo on my wrist 2 weeks before for my birthday?

No problem. Will not interfere with your procedure and may it go well and successfully.
Generally yes. Make sure it is performed at a clean tattoo center with a certified artist that uses sterile procedures. Also, be sure to ask the surgeon, just to be sure s/he agrees and approves, as they know your medical case best.