In short, I don't believe an problems would come by removing the 5th and 6th strings due to the lower tension of the classical strings. Yamaha classical necks are pretty beefy.
An alternative - I've converted some guitars to four stringers by utilizing string slots 2 thru 5 (removing strings 1 and 6) and arranging the strings as desired for what tunings I want. This keeps a more even, symmetrical tension on the neck, top, and bridge. However, I have done this only on steel string guitars for a make shift tenor guitar and not on one of my classical. Of course the steel stringers have a narrower nut width - a standard classical neck might have too much reach to get to the fifth string than you want.
An another alternate, relative to ampeep's post, I have a classical that I tune strings 5 and 6 as drone strings. Really, it's simply just tuning the 6th string to drop D. The result is DAD for strings 6, 5, and 4. I play the melody on the top four strings and use the fifth and sixth strings as drones. This sounds great for the Celtic music I like to play.
Just some ideas that hopefully you might be able to benefit from.