To cut a dash means to have a striking attractive and elegant appearance, but in this sentence he would look frumpy and unattractive
Consider the statement "Lady Cameron, he began, I am a simple country lord who doesn't want to spend the season in London and look very frumpy and unattractive among the upper class.". Is the statement "Lady cameron, he began, i am a simple country lord without any aspirations to spend the season in london and cut a dash among the ton." false? Yes/no/unknown