Yes, you can sand it. I'd recommend you try it on a scrap piece to give you the "finish" you are looking for. I'd start with 100 grit. (I think 60 might be a little too rough.) Travertine is a relatively soft stone. I used diamond pads and bullnosed it myself, but it was on larger pieces. I don't think you'd have to go much finer than 220#.
If that doesn't work, I'll always think it should have.