Seems, if your climate allows it, the most sustainable way to dry clothes is by hanging them on a line (though perhaps a particularly efficient dryer is used and it saves you time that you can use to be more efficient/sustainable than the time it takes to hang the clothes on the line...)
For clothespins, seems to me the more sustainable way to acquire clothespins is vintage ones (Craigslist/Etsy/Ebay). The older ones are strong and already exist in plenitude.
The most sustainable method of shaving that I've found is wet shaving with a vintage safety razor. It also seems to be the cheapest. Vintage razors can be found on Craigslist/Etsy/Ebay for cheap and the razors cost pennies. The blades can be recycled as scrap metal.
It's important to consider the brush as well. Many brushes use boar hair which as far as I can tell is not particularly humane or sustainable. https://www.vegan.com/shaving/ has suggestions for vegan brushes though I have not analyzed the materials...