I am holding a coffee in my right hand.
My left hand is free.
I remove my hat, which places it in my right hand.
I spill my coffee.
It makes for incredibly awkward situations that are played out IC. I mean IRL I am absolutely certain most people can take off a hand without throwing a drink all over themselves. I can only speak for myself, but working at a bar I used to regularly carry eight pint glasses without spilling a drop through a busy bar.
This goes double for those characters that are super humanly fast and precise with a weapon, yet fumble a cup of tea the moment they doff their hat.