I've updated all classes with skill points, but giving them far fewer skill points than specialists. Also, I have made separate skill lists for all classes, meaning that specialists still have the broadest access. I've also added the skills Riding, Medicine and Lore to the system, mainly due to requests from my players, as well as enabling all classes to put points into a "secondary" skill (basically most anything they really want, but it will always be something more limited in scope than the existing skills - the examples we have so far are smithing and farming).
I should say that the amount of skill points granted to non-specialists is very limited, except for the halfling who actually gets a skill point every level. Also, dwarves and elves (who get the fewest points to begin with) can use these points to increase their attack bonus instead, giving them a slight edge in combat (about +1 to hit for every 3/4 levels, if they want to skip skills entirely).
Works very well so far, although I haven't had time to playtest it thoroughly yet.