بسم الله الرحمن الرحيم
(Fatwa: 761/761/N=09/1436)
Alcohols which are prevalent nowadays are not prepared by grapes or dates rather they are prepared by various grains, vegetables, patrol and coal etc. And such alcohols as per Imam Abu Hanifah and Imam Abu Yusuf, may Allah have mercy upon them, neither are haram nor impure. So it is mentioned in the books of Fiqh and Fatawa. In this age, for the purpose of treatment and general use the Ulama have preferred the views of Imam Abu Hanifah and Imam Abu Yusuf, may Allah have mercy upon them. Principally, the opinion of the Shaikhain (Imam Abu Hanifah and Imam Abu Yusuf) are usually preferred. And in this case the basis on which the view of Imam Muhammad, may Allah have mercy upon him, was preferred it is generally inexistent in alcohol mixed things. Also as you said that alcohol is used in less quantity in cosmetic products, hence you may use it as per the Shariah, it is allowable. However, if someone avoids it then it is better and is his piety.
(در مختار و ردالمحتار 10:27-36، مطبوعه: مكتبه زكريا ديوبند، تكمله فتح الملهم 1:515، 516، 3:506، 507 مطبوعه: دار إحياء التراث العربي بيروت، فتاوى محموديه جديد ڈابھیل 18: 191، 192، منتخبات نظام الفتاوى 3: 385، كتاب الفتاوى 6: 205، احسن الفتاوى 2: 95، محمود الفتاوى 1: 362-364، 4: 379، 740، اسلام اور جديد معاشى مسائل 4: 11-13 بحواله فقهى مقالات، تكملة فتح الملهم اور انعام البارى).
Allah knows Best!
Darul Ifta,
Darul Uloom Deoband