The phrase 'お願いしてもよろしいでしょうか' can be translated to English in several nuanced ways depending on the context. In formal situations, 'May I ask a favor of you?' captures the polite hesitation perfectly. For a slightly more casual but still respectful tone, 'Would it be alright if I made a request?' works well.
Interestingly, the Japanese original carries a subtle humility that's challenging to replicate directly in English. The closest natural equivalent might be 'I hope it's not too much trouble, but could I ask you something?' - this preserves the original's considerate vibe without sounding overly stiff. The key is maintaining that balance between politeness and natural flow.