Do hand sanitizers that are used come under the same heading as the kinds of perfumes which it is not permissible for a woman to use if there are men around who could smell it?
Using hand sanitizers is permissible even if you get some smell like perfume as a result. The intent is to sterilize and sanitize, not to perfume yourself. Sterilization is an important medical necessity, according to medical safety protocols, so as to prevent the spread of disease and epidemics, and to protect wounds from infections and complications. This applies even if we assume that the prohibition is applicable in the scenario mentioned in the question, so how about when the conditions of prohibition are not applicable in that scenario? That is because the fragrance in hand sanitizers is very mild; it is not strong and does not spread widely, and it disappears within a few moments.