Dont worry about washing the one thats cut already, may mess things up. Besides I guarantee most of us smoke dust anyway haha.
You got the idea right, though I do a more vigorous shake under water to get everything out. Make sure you drain them nice and shake excess water off. Then get them hanging like you are and point a high power fan at em to start removing that excess moisture.
Also recommend 62% boveda packs and gallon mason jars. Curing is next after drying step.
Make sure you have plenty of water and change it often. A fish net is nice to scoop all the thistles etc off the top of water.
Only tips I can stress at this point is you need all ducks in a row from this point on, and control that humidity to lower it nice and slowly to get to curing.
Do not let buds hang wet without a fan or strong breeze, they can mold still.
I use propylene glycol which is a dehumidifying agent in a tub at bottom of a big cardboard box for drying. I ha e a humidistat reading internal humidity and monitor it until it reaches under 70 then I add to jars with boveda paxks and burp often until smelll stabilizes. If you wanna see it check out last years grow journal i called it box 2.0
I tend to overcomplicatw things but I like control so yknow do as much as youre comfy with.
Tldr: control that humidity from now til smokin