First, let me say I a totally on board with the no origin movie MCU Spider-man. However I can see a need to differentiate the pure Sony movie Spider-man origin with the new MCU Spider-man. They may want to include some origin stuff into the new Spider-man movie. To that effect I think they should go the Powerpuff Girls route.
That is a quick little montage at the beginning of the movie explaining Spider-man's origin and motivation. Something along the lines of "Bitten by a radioactive spider, high school student Peter Parker gained the speed, strength and powers of a spider. Adopting the name Spider-Man, Peter hoped to start a career using his new abilities. Taught that with great power comes great responsibility, Spidey has vowed to use his powers to help people." Read by Stan Lee of course.
Takes about a minute and the origin is done with during the credits and the very first scene could be Spider-man fighting Rhino or Shocker. No villain origin either. They didn't origin Nolan's Joker in Batman and that worked out fine. They could definitely do the same with second tier criminal.