Ay and/or Horemheb likely conspire to have Zannanza murdered the moment he arrives. Interestingly enough Horemheb was meant to be Tutankhamun's successor due to the latter's inability to produce an heir but he was likely outmaneuvered by Ay who ended up marrying Ankhesenamun. Also neither advisor ended up producing an heir, leading to his second-in-command Ramses I taking power. Let's say Zannanza is able to out-manuever both of them and use the other to solidify control; likely it would be Horemheb who seemed to have had an antagonistic relationship to Ay. Zannazana lives long enough to produces an heir with Ankhesenamun; Horemheb serves as regent and through the boy (call him Amenhotep V) maintains a steady course for Egypt. No 19th dynasty though maybe this Amenhotep V would marry into the Ramessides.
Due to Zannanza and Ankhesenamun's child being half-Hittite, expansion will be turned westward against the barbarian tribes of Libya and beat the Greeks into settling the coast. Relations will be cordial but there will likely be a confrontation at some point over Syria.