I agree, as his duel role as BP and monarch of Wakanda make him much more high profile in the MCU than Spidey is likely to be at that point.
I'm placing my bet on Spidey filling in the role of the New Warriors at the beginning (teenage superheroes that botch a villain takedown, causing massive amounts of property damage and civilian casualties), thereby prompting the Superhero Registration Act.
The film could start with him post-spider bite but pre-"Great Power and Responsibility". Instead of wanting to be a wrestler, have this iteration of Pete be inspired by the Avengers to be a SH out the gate; however, he lacks the maturity and training to be effective. Have him battle one his lesser foes we haven't seen yet that wouldn't take significant amount of time to explain (Kraven, Scorpion, Shocker, Vulture), and the resulting carnage (which Uncle Ben dies in) sets the CW story down it's path, as well as Pete's in his subsequent solo film.