I had been gathering old plastic bottles for some time to try making something out of high-density polyethylene (HDPE). This material can be melted in oven to make it soft, so that it can be molded to pretty much any shape.
After cutting the plastic bottles to small pieces to make them melt easier, i started with making the shaft. I intentionally made it about 10 cm longer than I needed so that I could saw off the extra part to make the hole in the mold exactly the right size. I also made one end of the shaft thicker, so I could hammer the shaft through the head tightly.
I made the mold by screwing four pieces of scrap wood to the shape of a rectangle, with a plywood bottom. I then screwed the extra part of the shaft to the center of the bottom.
I filled the mold with as much plastic I could fit in it, and placed it in the kitchen oven in 175 °C.
After half an hour or so, it had softened enough for me to push it to the bottom and add more plastic on top.
I repeated this a few times until the mold was full enough, then let it cool and disassembled the mold.
At this point I realized how ugly it looks, and decided that next time I will make it way larger than needed and saw the excess off with the table saw to make the edges smooth. Other than the looks, HDPE seemed to work really well as mallet material. It is denser than wood, which is always great.
I then hammered the shaft (which I had sanded and polished while waiting for the plastic to melt) through the hole. I took some work to get it all the way through, but at least I don’t have to worry about it ever coming off accidentally.
In conclusion, i was happy with how well the method worked, even though the mallet didn’t turn out that pretty. Making the hole with the extra piece of shaft worked really well. However, it was quite time-consuming to wait for the plastic to melt.
You may cover the mallet with big flakes of and use a heat gun to glue the flakes to the mallet. Could at least smoth the worst bumps of the surface.
You may also increase the size of the mallet by several layers of flakes and then use the table saw.