Answer
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.
In this fatwa:
It is permissible for Muslims to use hair gel that contains alcohol.
Answering your question, Sheikh Kifah Mustapha, the Imam and Director of The Prayer Center of Orland Park and representative for Dar El Fatwa of Lebanon in the US, states:
Yes, it is permissible for Muslims to use hair gel that contains alcohol. Alcohol is not allowable because it is an intoxicant.
However, it is not forbidden that alcohol touches the body because it is pure made from pure originated items like grapes, dates, rice or barely.
Using cologne, perfume, hair gel or soap or anything with alcohol in a matter of hygiene or beautification but not consumption should be fine.
Almighty Allah knows best.