Asking for preferred pronoun is gaining in popularity, at least in tertiary education circles. Something like the following could work:

I prefer to be referred to as:

• [ ] He / him
• [ ] She / her
• [ ] They / them

I'm a regular blood donor in Australia, and I'd say that donations here already follow most of that protocol. You are reminded when booking (and also via SMS on the day) to eat a meal and drink at least four glasses of water in the hours leading up to your donation, all donations are conducted in a reclining chair, and the staff (in my experience) are always incredibly friendly and empathetic. Apheresis donors also get a milkshake and a blanket during the donation, but those are more to prevent citrate reactions and the donor feeling cold when the slightly cooler blood is being returned.

Also, if you're one of the people with hard-to-find veins, they recently rolled out a technological solution for that too: http://www.techtimes.com/articles/19320/20141103/australian-red-cross-uses-new-technology-to-find-veins-no-more-poking-during-blood-donation.htm