Do you need to know the gender for a processing purpose, or just to make your narrative emails less awkward? Like, does it really matter for your job if Chris Smith is male or female, or do you just want to avoid writing, "We can provide him/her with XYZ services, if s/he completes ABC forms..."
In some places/industries asking about someone's gender and/or marking it down on their file (as the OP would have to as it sounds like there are too many to just remember) is illegal/otherwise not allowed. So if the only consequence is awkward him/her, s/he emails, I would just be awkward; and if the response indicates a gender ("Mr. Smith told me...") the OP could mark it down in the file, if that's allowed. If it really matters for the job (like, say, calculating medical insurance rates), I think it should be on the initial form/application. Etiquette-wise I don't think it's rude to do him/her, s/he if you aren't sure.