Prayer with alcohol-based perfume

Non-wine alcohol is not ritually impure. As a result, it is permitted in external uses, such as in perfumes and soaps. [Mufti Taqi Usmani, Takmilat Fath al-Mulhim; Shaykh Mustafa Zarqa, Fatawa]

It is, therefore, permitted to pray wearing such perfume or deodorant. However, one would be rewarded if one avoided it out of scrupulousness, though there is no intrinsic legal dislike in using them in the Hanafi school. This is because this is a matter of legal difference of opinion and it is recommended to avoid that which is genuinely differed upon.

Source: http://qa.sunnipath.com

A Fatwa of Deoband

It is lawful to buy and sell perfumes containing alcohol due the following reasons:

(1) Usually the alcohol that is mixed in the perfume is made of things that are not equivalent to khamar (alcoholic beverage) which is haram as per the holy Quran according to Imam Abu Hanifa (رحمة الله عليه).
(2) There is the probability that the nature of the substance changes after it undergoes the chemical process.
(3) It is used by the majority of people.

Note: If it is known that the alcohol mixed in a perfume is made of grapes or dates, then the use of that perfume and its dealing will not be lawful.

Allah (Subhana Wa Ta'ala) knows Best
Darul Ifta,
Source: Darul Uloom Deoband