With this improved clothespin design you are able to hang the clothespin on a towel hanger with a rod diameter of 14 mm.
You have to print this part on the side like it is shown in the picture.
To save some filament, you can use the counterpart from the original wooden clothespin from which you need the spring anyway.
I used partly the design from: https://www.thingiverse.com/thing:570467
Takes about 20 minutes to print.
Print on the side (like it is shown in the picture).