Look, you're not going to find many people who think that Nixon is a great name, and even fewer who like Nixyn. The y doesn't make it special, it just makes it look like you can't spell. It is your child and you should use whatever name you love. But be aware that if you name your daughter Nixyn, the reaction from most people will not be positive. It may be unfair, but it is true.
If you like androgynous names, I think that Brynn is much better. There are also lots of other named in this vein: Arden, Sloane, Blair, Harper, Greer, Darby, Darcy, Marlo, Shea, etc.
I think that having two children with x names is a bit matchy. But if you like the spiky sound of an unusual consonant you might like: Ever, Roxanna, Zora, or Zelda.
[Edit: Sorry, it takes me a long time to type, so I didn't see your other replies before I wrote the first paragraph.]