The straps will all have had buckles originally, though I do like the infinite adjustability of a deployant clasp myself too. All my TAG Carreras have clasps and my 510.511 Carrera is actually on a TH strap with deployant too - not original, but it is a black leather strap with orange contrast stitching that fits well with the orange hands on the watch.

Good luck finding a nice strap - the spring bars are pretty accessible on this case, so you could even get a selection and see which suits best and maybe change them when the mood changes too.