How soon is it okay to have a solo orgasm after laparoscopic bilateral salpingectomy without increasing the risk of sterilisation failure?

Anytime: There is nothing that I know of where an orgasm would cause a failure of your sterilization procedure. Especially, since it was a salpingectomy.

Right away: There is no risk of failure of sterilization from just having an orgasm from masturbation. Also - if you had a laparoscopic bilateral salpingectomy - where they actually removed your tubes - you are immediately sterilized from that procedure. It is also the most effective method of sterilization.