hi katana,
found that 1.5mm 'carriage' cane strips used in reweaving cane chair seats is split from rattan. can find that on the internet in 25ft. thru 1000 ft. spools, the latter may be a bit more than you need
i gather in thailand/burma, in the areas they make dhas/darbs that the little old ladies of the family sit around making the rings in a range fairly std sizes so they can be slipped over the grips & adjusted into place without too much fuss.
i imagine the supply of similar little old ladies in your area may be a bit limited tho, which is why i suggested using some lengths of flat braided twine (non-fuzzy type) of roughly the same color.
here's one i prepared earlier (it's on a long (1.25in. dia) shafted Cold Steel Assegai) i used a fairly coarse organic string to improve the grip as i was not trying to match anything, the ends of the spirally wound area were pulled back under the last few turns & cut off, the whole was 'varnished' by soaking in extra virgin olive oil which dried nicely after a few weeks. the spear shaft was also so treated.