If you're a creative person and a jack-of-all-trades, chances are that you've given woodworking a try at some point in the past, or you intend to get your hands dirty with wood filings in the future.
Mount the wood piece on the lathe chuck and use a roughing gouge to shape the square into a cylinder. For the handles, you can use a parting tool and calipers to size them before applying the roughing ...