Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, thanks a lot for your question which reflects your care to have a clear view of the teachings of Islam. Allah commands Muslims to refer to people of knowledge to get themselves well-acquainted with the teachings of Islam as well as all aspects of life.
As far as Islamic Shari`ah is concerned, it is forbidden to drink alcohol. However, being forbidden does not mean it is impure according to some Muslim scholars. Other Muslim scholars are of the opinion that it is impure and therefore, internal or external use of alcohol is forbidden.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto,Ontario, Canada, states:
There are two views on this issue among scholars and jurists: One group holds the view that alcohol in any form or condition is clearly unclean and forbidden, and therefore cannot be used in any way, and not merely internally.
However, there is a second view. This opinion is held by those who do not consider alcohol to be unclean in itself, and as such they do not consider its external use to be forbidden. Some of them also point out that the alcohol found in aftershave is such a small percentage that it evaporates quickly, and therefore one does not need to be overly rigid about it. Therefore, they rightly conclude that it is permissible to use aftershave or cologne with alcohol contents.
Having said this, I must also point out that if alternatives are available, we are best advised to use them.
Excerpted with slight modifications from Islam.ca.