For something like this if you really need it to be 100% physics you could use Houdini.
For anything, but 100% real you could rig a bill with some bones and do some quick hand animation. With something like ghost ik it could go really fast.
One set of bones along the long side is where most of the bending of the bill will be. The other side is too short to get much bending most of the time. Maybe combine that with rigid body physics.
