Statistically we know that across the board, men get more resumes accepted than women even in people who believe they’re being fair and equal. Even women, who also make up the bulk of Human Resource positions, do this. But you have to balance your job prospects against your identity and your life, and sometimes it’s worth it to make something a little test of whether you even want to work there.
I think for admin positions, which as you say are predominantly female filled, you could probably get away with it, and if you have a strong feeling about using both your names, then you should use them both. It’s easy to say “your identity is more important than whether you get a job” from the position of a well-paid benefits-able job; harder to say that when I put myself in your position. And this contrasts with the advice I just gave about queer identity. But there’s also the fact that you’re expected to give a name, and the name carries a weightload of information about you.
Again — this is a decision only you can make, based on your feelings about your name, the qualifications you do or don’t have for the job, and the fact that this is the kind of job people don’t expect to find many men in. My advice would be to use both names, especially since it’s important to you, but it has to be your choice.