There are a whole lot of styles that I'd like to be gone - plus over 33,000 files along with them. I'd like to have only L1, L2, L3, and SMS Sega styles only. What happens when I delete the others? Well, I get an error message and cannot play the levels.
Make sure you're not deleting the "default", "xmas" or "special" styles. In particular, NeoLemmix will not take kindly to the absence of "default" (the other two won't cause problems until you try to play a level that actually uses them), as it contains several objects shared between multiple styles (eg. the common hatch and water shared by Dirt and Pillar; the generic recolorable one-way-arrows) and the placeholder pieces used as fallbacks in preview images if pieces are missing, not to mention the actual lemming sprites. Xmas contains the lemming sprites and objects from the Xmas/Holiday Lemmings games (the terrain pieces are mostly identical to ohno_snow, and the few that aren't have been merged into ohno_snow in NL), while Special is for the special graphics levels (like A Beast Of A Level).
(It is technically possible to create a level that doesn't need the default style, but it's easier to just assume that
every level requires it.)
At any rate, if you're distributing your content you only need to distribute the levels, music, and any custom styles you make for it (if you don't get these added to the Style Manager / all styles ZIP). People looking to play your packs should already have (or easily be able to obtain) everything else. You certianly don't need to include every style that exists.