There is no doubt that Islam urges people to keep themselves pretty, tidy, and clean. We have references in the Qur’an and hadith that prove that. As for the point you have raised, some Muslim scholars say that wearing alcohol-based perfumes is allowed in Islam.
In this regard, Al-Azhar House of Fatwa issued the following: “In Islam, it is unanimously held that all things are supposed to be deemed pure, and that it is not necessary that all what is declared forbidden is considered impure. This is because impurity is a legal ruling that needs evidence. For example, drugs and fatal poisons are forbidden, yet this by no means qualify them to be impure.
For this reason, some scholars including Rabi`ah, Al-Layth Ibn Sa`d, Al-Muzani (the companion of Ash-Shafi`i) and some other scholars hold that wine is pure regardless of its being unlawful, and that only drinking it is forbidden. However, the majority of jurists are of the view that wine is impure and forbidden.
thus, we conclude that all that is impure is deemed forbidden, but not vice versa. This is because regarding something as impure is to forbid any physical contact with it, whereas regarding something as unlawful is not necessarily to forbid any contact with it. To illustrate, wearing gold and silk is unlawful (for men), yet they are considered pure by the consensus of scholars and thus can be touched by men.
As far as perfumes containing alcohol is concerned, they consist of many ingredients like water, perfume, and alcohol that comprises the highest percentage. It is known that alcohol is produced from sugarcane by way of distillation. Thus, according to the juristic rule, which states that all things are presumed to be originally pure and that being prohibited does not render something impure, perfumes that contain alcohol are pure, particularly if we bear in mind that they are used for cleaning and perfuming the body. Thus, it is permissible to use these perfumes and there is nothing wrong in that.”
Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, adds:
“It is forbidden to drink alcohol. In the perfumes usually denatured alcohol is used. This alcohol is not unclean (najas). According to some jurists even natural alcohol is not najas. According to the Shari`ah, there is nothing wrong in using alcohol-based perfumes.”