If the deodrants/perfume is made from synthetic/chemical alcohol, extracted and manufactured from items besides grapes or dates, then the use of such products is permissible.
Hazrat Mufti M. Taqi Usmani Saheb, (A leading contemporary scholar of Pakistan) writes in his commentary of Sahih Muslim, "The majority of alcohol used in medication and perfumes is not manufactured from grapes and dates, it is extracted from grains, peels or petroleum etc." (Takmilah Fathul-Mulhim Vol. 3 Page. 608)
Before using such products, it is advisable from the Shar'ee point of view to check with the manufacturers on the type of alcohol used. (i.e. whether natural or synthetic based).
Allah SWT Knows Best.
(Mufti) Abdullah Patel