I do not recommend doing this.
Each time I washed it salt would recrystallize as it dried, so after 3 washes I decided to soak it in a lot of water which resolved that.
Then I went to use the salt and without any salt build up it poured out way quicker and ruined my breakfast.
When I do mine, rather than soaking them until the salt dissolves, I’ll put a bunch of elbow grease in with a damp paper towel. It’s less washing and more polishing. Perhaps the limited moisture from the paper towel helps? The dry part of the paper towel helps remove moisture as I clean it?
SAY MOISTURE ONE MORE TIME.
The lid has plastic parts for a spout and you can’t get into where the plastic and metal join or the hinge of the spout, that’s where the salt send to have set up base.
Ah … I think new shakers are in order then.