That’s the question…
How do you dry it? I just use to cover the windway, blow hard into the mouthpiece and then shake it a few times.
What do you do?
I normally take off the mouthpiece, pass a weighted cloth through the tube, and then use a large pipe cleaner thing to clean out the mouthpiece. They can both be purchased at a local music shop. I usually only do the blowing thing to clear out the moisture while playing.
The same as you. Sometimes I wipe the outside with a soft cloth. Sometimes I swab the bore using a recorder bore brush, or a cleaning rod with a piece of soft chamois.
With wood whistles you have to be careful about covering the windway with your hand or finger. Touching the blade/labium when it is wet can, over time, deform it. Recoder players remove the head, cover the bore end with the hand, then cover the window with the mouth and blow to expel moisture out through the windway.
But I disassemble my (metal) whistles as infrequently as possible. IMO, the risk of damage outweighs any advantage of constant cleaning.
By the way, my method is based on wooden whistles, when I need to get all that moisture out definitively.
Blow through but do not shake it if it is a tunable one, just in case the head gets loose.
Brigitte
Simply hold it securely with your hand around the tuning joint before shaking it out. And watch where you’re pointing! 
Stand them up on end and allow them to dry naturally.
I use a pen holder/desk tidy I bought from an office supplies shop to stand my whistles in.
One hour in the tumble drier!
Oh behalf of all the wooden whistle makers, I thank you! 
I use a cotton bandanna rolled diagonally and twisted into the bore of the whistle. With no hard parts, there’s no chance of damaging the blade as Guru wisely warns against.
I have a one-piece maple low G. What’s a good way to dry that?
MT Guru wrote:
I dissasemble my (metal) whistles as infrequently as possible, IMO the risk of damage outweighs and advantage of constant cleaning
While I would agree that it is debatable weather a whistle needs frequent cleaning or not, I must respectfully disagree with that statement. (to a degree) I take apart my metal and plastic whistles after every extended practice session. I do it carefully, then wash out the fipple in soapy water, dry with a rolled up hankerchief and put back together with a bit of Susato’s joint grease. After nearly two years of doing this almost daily, none of my whistles show any sign of wear or loosness in the fipple. the whole procedure takes me about five minutes per whistle and I know that I will always have a clean, nice playing (no gunk in windway) whistle every time… Just my observation…
I just shake it and let it dry outside of its case.
I wait until the bodhran player is watching and then I pound the end of the whistle into my knee, leaving an unsightly dribble mark. The guy is like 6’ 7", covered in tattoos, wears spurs to session (we don’t have cowboys here) and has hair becoming to a Death Metal band. Every time he sees me do this he squeals “Eeeeewwww” in a voice higher than my six year old daughter’s. Bleedin’ priceless. 
ROFL … Squirting tea through nose … 
Please Mr. Bodhrán Player, sir, sit right here. Pound away, oh please do. Have a biscuit. More cowbell, please, if you have one …
Lightheaded Mike, hit the nail on the head, turn towards bodhran player, grip whistle up near the mouthpiece, raise whistle above head and bring it down very fast in an arc to about knee height. This will ensure that all moisture in the whistle will go to a deserving benefactor, as in the said bodhran player. The beauty of doing this is that they will get used to you doing this and will in time move away to another part of the session and you won’t be put off by their thumpity-thump that does nothing for your feel of the music.
How about a gun cleaning rod and maybe a 2x1 linen patch?
–James
Emmmmmm, Why would you want to dry out your whistle?
I never dry mine, chuck them straight into my carry bag and off I go, doesn’t do them any harm, they still sound great.
I don’t know why I take so many whistles with me, I invariably end up using only my Gen’ d.
Along the same lines, a tenor recorder cleaning rod or brush swab would probably work.
Feathers are pretty good for the windway and if you use duck feathers get a moisture repellant bonus too.
Finger over the window and blow hard,
wipe the outside on the nearest set of curtains
If anybody looks or says anything I ask “What?” 