We don't actually know what happened to left-handed people in Greek warfare. It is never discussed in any source. There is no evidence that it was ever a problem. If we can take it for granted that left-handed people do universally exist, we should probably assume that left-handed hoplites were made to fight with their non-dominant hand, and that they would be pretty bad at it. Greek hoplites generally didn't train to fight in armour, though, so the left-handed hoplite would be only marginally worse at it than his neighbours. Skill at arms was not considered very important in mass hoplite battle.

What you said about the importance of the shield to cover the man next to you is based on a misinterpretation of a single passage in Thucydides. There is nothing to suggest that a hoplite's shield covered anyone but the hoplite himself. For a long time their combat stance was wrongly modeled as head-on (directly facing the enemy), in which case a round shield held by the left arm would stick out well to the left of each hoplite. But this stance is very awkward, unnatural, impractical and exhausting. The actual combat stance shown on vases and reliefs is a three-quarters or sideways-on stance, in which the left foot and shoulder point to the enemy while the right side is kept back, and the shield rests on the left shoulder. In this stance, a big round shield held by a double grip actually aligns with the body's centre mass and covers a single warrior perfectly.

In this sense it should be possible for a hoplite to be left-handed without messing up the line of shields. If we also assume (with scholars like Hans van Wees) that the phalanx was usually a lot more widely spaced than most modern reconstructions suggest, then our left-handed hoplite could even take his reverse stance without really getting in the way of the warrior to his right. But, as I said, we have no evidence that this ever happened. Why not?

It's probably because there were other reasons why it mattered that all the hoplites had their shields on the same side. I go into more detail in this old thread. Both the movement of the phalanx and its safety on the march relied on there being a guarded and a "naked" side to the whole collective.