I used to rinse and then let dry, but when I found some tea staining on one of my Timeless Razors when I went to put in a new blade, I decided I needed to start disassembling my razor. So that's what I do now. I loosen the razor a bit to rinse it, put it aside, finish drying brush and putting away products, and then take my razor and a microfiber cloth and sit down and disassemble it completely drying the blade, and each component separately. Then I'll reassemble the razor partially to keep it together and put it up.
Joe