If it's ceramic tile, I would assume you could have someone come out and "reglaze" it (not sure about the term of art) . I did this with my cast iron tub, and it turned out great.

I saw some decorative stick on tiles at Home Depot a while ago, that were accent tiles. They were modern, some looked like stainless steel. you could try those on top of the tiles you have if they would stick. Not sure if your floral tiles are textured or flat. They may not stick in the shower area though. I have also heard of special paint for ceramic tiles too. you could try that in a coordinating gray colour.

TileWorks is spot on correct. If you're skeptical about being able to do it, call a tile store - one that specializes in flooring, usually - and ask them to recommend a local contractor. It really isn't going to cost that much to have it replaced professionally.

If you are going to go to the expense of cutting out and replacing tile, you may wish to reconsider a bigger bathroom renovation (if it is on the plans); this is quite a lot of tricky labour work. Failing that, buy bathroom paint and paint the band in black) - this is a temporary fix and not a long term one

We make hand made tiles and can make for you a border that will be like a quarter round that can be fairly easily installed over the existing border you have now

I think cutting out the tile is too risky?!? I can not afford to renovate bathroom at the moment.