system agnostic: How can I handle my DM's requirement to play a female character in her one-shot when I'm not comfortable doing it?

Role-playing games should be fun for everyone involved. If you really feel uncomfortable with this, the DM should not ask you to do it. As always is the best advice, you should speak respectfully with the DM outside the game and explain that this is not something you want to do.

If you still insist that you must play a female character against your wishes, you have two options:

  1. Do not play This is not the game for you. Explain that you do not feel comfortable participating and expect them to have fun at one time.
  2. Make the best of it. If you are able to overcome the discomfort, this could be a great opportunity to play outside your normal character. We have a great question on this site that includes techniques to interpret a woman as a man. I suggest you consult it to get better advice than I could give.

Personal experience

About 6 months ago, my main character decided to leave the party for key reasons of the story. To continue playing in the next sessions, the DM suggested that I should take care of the female NPC that was traveling with our group. Initially, I had doubts about playing a woman full time. I had done it as a DM but never as a player.

After I started playing, the fact that the character was female was not a problem. I got attached to the character and I still interpret it. I am not saying that this will happen to you, but if you are willing to try it, it may be easier than you think.