恐れ入ります、ネギ抜きでお願いできますか？ — Excuse me, could I ask for it without green onions? (Ramen · Shop, Formal — to staff, JLPT N5)

Gesture & etiquette

Slight bow, polite hand gesture towards the server.

If you have severe allergies, it's safer to mention it specifically, e.g., 「アレルギーがあるので、ネギは入れないでください。」(Arerugī ga aru no de, negi wa irenaide kudasai. - I have an allergy, so please don't add green onions). However, for simple dislikes, 'nuki de' is sufficient.