You shouldn't have any problem inflating a Schrader valve tube to 100 psi. It may be more difficult to do (you have to push the air passed the spring-loaded valve in a Schrader, which is not the case with Presta), but it's not impossible. The bike will ride like a rock with that sort of pressure, and you may or may not actually be faster. There is a point of diminishing returns regarding tire with and inflation pressure, beyond which you're just making the bike less comfortable. In general, a quality 35mm tire inflated to reasonable levels isn't going to be slowing many non-professional riders down. Narrower tires feel faster (and may even be faster in some settings), but data shows that there just isn't a significant difference. Professional riders have been increasing tire width for a number of years now, even riding 30-32mm tires lately. It's mostly just personal preference.
I agree with
xroadcharlie that
different tires in the same size will be as transformative as
narrower tires.