Nappa would probably follow Galu and Vegeta to the site of their battle. The ensuing events drastically differ whether Nappa puts his Scouter back on or not (since he didn't destroy it like Vegeta did). With the Scouter, he notices Yajirobe hiding nearby and kills him, although is killed himself by Vegeta when he tries to intervene when Vegeta gets his ass kicked by KKx3 Galu. After this, the Z Senshi aren't able to cut off Vegeta's tail without Yajirobe and are all killed by Oozaru Vegeta. Vegeta then kills all of mankind in a month or two, before arriving at Planet Freeza 079 to discover that Freeza has killed off all the Namekians when they refused to let him use the Dragon Balls. Vegeta never escapes servitude and the Freeza Force are eventually taken out by Babidi's forces when they convene on Earth and take the planet away from Freeza.
If Nappa doesn't have his Scouter, then things more or less go the way they did in canon due to Nappa not targeting Gohan or Kuririn and likely just being killed by Vegeta for intervening when Galu rapes him.