I started to suggest that approch Soquili but then I realized that it won't work, at least not very accurately. You'd have to do each word individually for it to look half way close. Keep your text string down to 5-8 letters on each curve before molding.

I don't think it's gonna be easy, which ever way you try. Perhaps you could sit the watch on a scanner & scan it high rez, then trace the text manually.