I assume most warriors with swords or shields were right handed, but I imagine a left-handed warrior would have a more difficult time during combat. Were there any advantages to being a different handiness that the majority? Or was life generally more difficult?
This has come up before, but unfortunately, there doesn't seem to be much info on it. As is pointed out there, we have reason to believe that in a military based on shield formation, lefties would be forces to fight right handed, but that's about it.
As I said in that thread, for single combat - or at least as you'll see in fencing - though, there is a real advantage to left-handed fencers, but (as far as I'm aware) it isn't because they are intrinsically better or have more of a killer instinct. The main advantage is because a left-handed fencer is very used to fencing against right handed-fencers on a daily basis. On the other hand right-handed fencers practice against lefties very rarely.
A right-handed fencer who practices against lefties on a regular basis would essentially eliminate that advantage. Likewise, if a club was all lefties, so never fenced right-handed people, that advantage would mostly disappear.