I don't think so, it can be done neatly. If the real main stake is the Night King, Aegon can basically be in the background, a distraction people aren't paying much attention to, a mere rumor of Aegon's return, which the viewer assumes is a misunderstanding that people are somehow hearing about and which has to do with Jon, something Varys could do to create doubt in Daenerys' mind towards Jon if not outright animosity but in reality to prepare the throne for the other Aegon, but you wouldn't see Aegon, you'd think it's about Jon. The war against the Night King rages on, with the Golden Company's help at Cersei's service, and we keep hearing mounting stories about Aegon's return thinking it has to do with Jon, so the viewer thinks Jon will be the hero who the people will put on the throne, and then when the Night King is defeated and the kingdoms are left severely weakened, after Jon/Daenerys saves the day but probably in a way that most people wouldn't really know about, the Golden Company betrays Cersei (if not during the war), and puts Aegon on the throne, and people know no better. Daenerys is pissed, wants to take it, and who knows what Jon decides to do, but I would think he doesn't let her. Bran knows Aegon isn't the real deal, but him and Jon let it be.
Jon doesn't look anything like a Targ, but Aegon would. People are dumb, Jon has no claim to them, any attempt to claim the throne at that point would paint him as an usurper. It puts him in a situation similar to the one Ned was in, and he has to make a choice. I think it ties things up nicely with what set all of the events in motion. It's all about the opening scene of ep1.
