You used both hands in a phalanx, one for shield, one for spear. Just as a right-hander would need to learn left-handed shield work, a left-hander would need to learn right-handed spear work.

If your right hand was simply useless for anything, you would probably be better of as an irregular or skirmisher, which were, if anything, more numerous than hoplites (who were by definition those wealthy enough to own armour).

If you were wealthy and hopeless with your right hand, then you would probably be relegated to the rear ranks. These did not simply stand around waiting their turn, but forcibly pushed the phalanx forward into the opposing shield wall, trying to force it to break. Only the first 2 or 3 ranks could be involved with fighting, but phalanxes were often 8 ranks (or even 16) deep, with the remaining ranks being the pushers.