Answered by Shaykh Faraz Rabbani
Question : What is your opinion on using perfumes/deodorants/after shave with alcohol content in it?
Answer: In the Hanafi school:
1. Wine is filth (najis) and unconditionally impermissible to consume or use.
2. Other alcohol is impermissible if used for intoxication; or in an amount that intoxicates; or as intoxicants are used; or for vain purposes.
3. Thus, external uses of non-wine alcohol are permitted, and so is the incidental presence of non-wine alcohol in food ingredients (such as in vanilla, which is often extracted using alcohol; or soy sauce, which incidentally contains alcohol)–when not used for intoxication, nor in an amount that intoxicates, nor used as intoxicants are used, nor for some other reprehensible purpose.
[ref: Ibn Abidin, Radd al-Muhtar; Imam Muhammad Bakhit al-Muti`i; Mufti Mahmoud Ashraf Usmani; Mufti Taqi Usmani, Qadaya Fiqhiyya Mu`asira]
And Allah alone gives success.