2) Flaming - contractor will heat surface with a torch and then spray water on the hot stone causing some areas to flake off. This provides a very elegant appearance which is very smooth to the touch but has a lot of texture for grip. This will likely be the most expensive solution.
For what it's worth, we just redid our pool deck with granite pavers with a thermal surface finish, and I would highly recommend it. It is very much non-skid - seems like almost the perfect kind of surface for a pool deck. I have no idea how well it works with travertine as opposed to granite, but if the "replace" option doesn't work out, this might be a reasonable Plan B for you to consider....