In addition to undrentide-san's explanation, probably as you already know, Gin uses Kansai dialect. This 泣かんでも is originated from Kansai dialect. (Or rather, ん, which is originated from Classical Japanese, still remains in Kansai dialect.)
泣かんでも済む means 泣かなくても済む/泣かなくてもいい "don't need to cry". 済む doesn't mean "to finish something" here.