The alcohol used in body sprays is not the same as alcohol consumed as a drink. Also, it is not alcohol extracted from dates or grapes and it evaporates. Therefore, to use it would be permissible. However, some scholars prefer that one uses precautionary measures by applying it from a distance so it doesn't stain the clothing, and to avoid using it at prayer times.
This response is credited to Mufti Yaseen Shaikh Sahib.