It would be easy enough to do, although the beginning and ending are the hard part. I have a lot of experience with wrapping bowstrings and the same problem exists there- how do you begin and end the wrap. There are a lot of wrapping videos on youtube and also a lot of sites/blogs on the net dedicated to paracord knots and wraps so if you watch enough you might find where someone has figured it out already.
What I would do is lay the cord next to the curved part of the handle and start wrapping, so you are wrapping over the end to anchor it in place, do this until you have covered half of the length. Now wrap a blob of cord in reverse over the very end of the curve leaving a loose loop between that part and where you finished wrapping in the middle, lay the other end of the cord against the remaining part of the curve. Now continue wrapping from the middle part of the handle to the end using the loose loop. As you wrap in the middle you are unwrapping from the blob at the end of the cord and the goal is to finish wrapping all the way to the end just as the blob that you previously had at the end is depleted. Now you grab the end of the cord that is protruding from the middle of the handle and pull it so the loop all pulls underneath the wraps and disappears. It might require some test runs to figure out how many wraps to put where.