My two directions I have narrowed it down to are
MX and Iota
Iota is a term that means "an extremely small amount" and is also the 9th letter of the greek alphabet. I wanted to use the small amount angle as a conceptual device for you wouldn't need a lot of this product for it too work. If it were for products after the shower then it could be something you use a little of and can use quickly if you are in a rush. The 9th letter of the alphabet aspect could be used as a visual device. Maybe mess with some serif typefaces and the colors of Greece, a light blue that could easily be gender neutral and go both ways.
MX is the proper term for a transgender person. Instead of Mr. or Mrs. it would be MX. I think that this would be great for a gender neutral product. There is the concern that it might steer some people away but I don't think that this is that much of an issue. Most people don't know that this is a term for a transgender person and the people who do know would appreciate it I think, especially if it was marketed as a product for all people. I think the name MX is also easy to say or relate to.
I think both could turn out to be successful and have potential. Overall I would like to go with a very clean, sophisticated, sleek look.