We were at both spring & fall last year and you will NOT be outnumbered, there will be a lot of people dressed up, but there's still a very high number of regular dressed guests.
The most dapper crowds last spring were at the grand floridian where evening drinks were "scheduled"
Also keep in mind that the parks change with the season.
I'm pretty sure spring wdw dapper day this year is Epcot, so crowds wouldn't be impacted much at all.(and they usually aren't)
Crowds with dapper day also usually are not doing your regular rides and such, they'll watch some entertainment, do the scheduled meet ups (which those, will be crowded, one of them last spring was a dapper ride on the people mover and the line was INSANE), and take a bunch of pictures. It shouldn't really effect your day