The expression とめてくれないか seems like negative indeed. But it actually means an affirmative action. It is a little similar to an English expression "(not) mind ...ing", which is literally negative but what it actually means is quite positive (like "agree to do something"). I guess you already know that "～ませんか？" sounds more moderate and sometimes politer than "～ますか？" in Japanese. The same connotation applies here. "とめてくれないかな" sounds more moderate than "とめてくれるかな". For your information, when you would like to form a negative sentence, you can say "あのラジオをとめないで（おいて）くれるかな" or "あのラジオをとめないで（おいて）くれないかな"　 (though the latter is quite confusing as it seems double-negative).