What's that word for the action you do right after rinsing and wringing a shirt, but before setting it out to dry?

This is really funny, but I'm writing a story, and need to describe an action I've done and seen others do almost all my life - here in Uganda at least, but I can't seem to find the word or expression for it!

Basically, as part of the process of washing most clothes, especially shirts/t-shirts, after one had finished washing the fabric in water, right after the final rinsing (not using a machine, but bare hands), and right before placing the fabric on a hangar or wire to let it dry, there's this action we do:

for a shirt for example, you hold it by its base on both ends, and doing a motion as though using the shirt to blow out a fire, cause more water to be lost from the fabric, and also to help lessen the possibility of creases forming in the fabric prior to hanging it out to dry.

It's the above act that I can't find the right word(s) for, and if anyone here knows of or has seen this act being done, maybe they might offer some suggestions?

Note: I'm almost close to 30, but don't think I've ever heard anyone describe that action with a word, yet it's so common [here] :-)

Consider to shake out. Example usages:

If you don't have time to fold a load immediately, shake out the pieces and lay them flat in the laundry basket (CNN)

Shake out clothes when you remove them from the washer. (NJ Laundromats)

Shake out clothes from wringer and drop into fresh, warm suds. (Approved Methods for Home Laundering)

I call this whipping...essentially one makes a small snap that is akin to cracking a whip. The speed of which expels water very quickly and smoothens the fabric.