Dan, I bought rattan from a craft/hobby shop. It is chair caning and comes in widths of 1/16", 1/8" and 3/16". The thinner the rattan is the longer of a piece you need. The 1/16" uses about 17" for a 4" handle and the 3/16" uses about 8' for a 4" handle. It can be spliced but one continuous piece works and looks better.
You can also use basket weaving material for handle wraps and it comes in more varied sizes.
When I use rattan I soak it in warm water for a while to make it more flexible, blot it dry and begin wrapping over the tucked end. At the other end of the wrap tuck it back under the last 3 or 4 wraps, pull tight and let it dry overnight. When dry, cut the tag ends off. I like to add a bit of super glue around the top and bottom edges of the handle and a little between some of the other wraps. Pat