Why would Katarina ever bring an instrument during a combat?

Yep, you explained perfectly what I meant! +1

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The original line is "Violence solves everything."

"Violin" would be the equivalent of dropping the "ce" from "violence;" the pun is awkward and can't mimic the original line without the double occurrence of the "s" sound that "ce" creates beside the "s" in "solves." Therefore, to keep the pun correct, you need to pluralize "violin" to be "violins."

Just say them side by side. Violence. Violins. They're practically the same phonetic word. However, violin and violence are not. Without the "s" on "violin," the stress on the word is on "lin" and not the "s" at the end like in "violence." Therefore, this is a bad pun, and not bad in the eye-rolling begrudgingly humorous way.

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You are making the wrong comparison. Everyone would probably agree that "violins solves everything" is better than violin solves everything" . . . unfortunately, that first one is not a practical choice because "solves" only is proper with a singular noun like "violin" not "violins."

The actual choice made by the author is between "violins solve everything" and "violin solves everything" in which case, the latter (and original choice) of the author is the superior one.

Just listen to this. https://www.youtube.com/watch?v=U6HnoPAykwU

The S (or ce) of violence is the same pronounciation as the S from solves so you won't hear the difference when you drop one of the two S sounds as the words flow into the next one. This makes "violin solves" sound almost perfectly like "violence solves". "violins solves" is grammatically incorrect. "Violins solve everything" loses the S at the end of solves without being followed by an S in the next word which makes it a problem.