The percentage of left-handedness correlates strongly with how pacifist vs warlike the society is. According to this 2005 study it varies from 3% up to 27%: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1634940/
Where I am going with this is that it might not be that left handedness directly correlates with violence in any way - but perhaps societies with more left handed people were simply more likely to survive in more war like times.
Which is still higher than average, and around the level seen in more violent societies. I think it makes sense that it wouldn't get up to 50% since you're sampling from a smaller pool in the first place.
Overall probably just really hard to get good universal data on this. I'm curious about fencing though. Another sport I don't know much about.