brown is another 'neutral' color that works with black and white scheme. Would be helpful if you can provide photos or links to the samples you have chosen.

Did you mean to attach a picture?

These chairs are easy to recover and the range of fabric available today gives you plenty of choice. I say go for it. If you don't feel up to it yourself get an upholsterer, but plenty of YouTube tutorials about.

Something to take into cosideration would be the amount of light you have coming into the bathroom. Obviously if you have considerable light and air the tile shade wouldn't be too much of an issue. On the other hand if the room is small and not very light filled, then the lighter shades would be preferable giving the illusion of making the room appear bigger and lighter.