Buy sticker samples from Samplize. Put on the wall (best if wall is primed white first so that the existing wall color does not distort/change the way you perceive the color samples) - compare the two colors at different times of the day, with lights on vs no lights, and move the samples around as colors can look different on one wall vs another.

they are both plenty dark for a small room with no natural light.

cutting paint % is fine when you get all the paint you need mixed by the same person(they have their own way of mixing) and mixed together in a large bucket... But if you run short and need a bit more mixed, you may run into a color change.

Have you sampled the colors in the room in all light?

It's always a good idea to get larger samples before choosing, like the Samplize samples. DH bought a piece of drywall and cut it into four pieces and we use them to try various colors. You may not want to do this if you're only painting a bathroom, but if you're going to end up painting several rooms you can use them over and over. I have sometimes thought I had the right color but after seeing it on a larger expanse, changed my mind. That size of sample gives you a better idea than a chip or even a Samplize sample does. Be sure to paint two coats so you get the kind of coverage you would end up with on a finished wall.

In general, I find paint colors look more intense on walls than you expect, so if you want to go right to painting your walls, I would try Pale Smoke first. Almost anything goes with black and white, so the odds are this will look fine.

Pale Smoke has more green in it . I use large poster boards aith 2 coats of each color and just get sample cans to start. I do 25-50% cut on BM Healing Aloe often but I aslo get the paint mixed all at the same time and added to a big bucket and stirred often during painting. So you can do the same with those . I love gray but I use C2 Vancouver Day for my living spaces it is just a hint of gray and honestly until you see it next to pure white it looks white . Only you can tell what works in your space with your lighting, BTW I use all LED 4000K lighting all over my house some on dimmers if needed .

Yes there is natural light in the room and even from a small window it is enough.

I like the idea of blue with your black and white tile floor. Your bathroom sounds nice.

White walls would also work, its what we did in our bath similar to yours with all white marble. Solid gray floors is the only difference instead of the basketweave. Feels very open in white paint.

You could consider a gray and white basketweave instead of b/w. Our gray really picks up the gray veining in the marble nicely.

I’m having the same issue. I have black and white floors and considering smoke in that entry and pale smoke in two adjacent ent rooms ps try and utility. I love layering color, but I don’t always get it right. Good luck sounds beautiful either way!