Anonsi, I couldn't find this word in any dictionary - I looked for both drummy and drummie. But some dictionaries do have drumette, a word already accepted in Chi. For example, the American Heritage Dictionary: "The small fleshy part of a chicken wing, often fried and served as an appetizer."
And usage seems to strongly prefer drumettes to drummies. The Corpus of Contemporary American English has 18 examples of drumettes, while the one use of drummies was unrelated to chicken wings (referring instead to an Irish town called Dundrum).
So, I find drummies to be too rare. (And, frankly, I won't eat a chicken wing unless it's well done.) So, fortunately, I don't have to decide whether the singular is drummy or drummie.