Anyone, with a physical body, can make an unarmed strike, and not use their fist.
This "fist only" thing comes from, well, nowhere, and does not exist.
Shields, and Armor, have no effect on unarmed strikes, or two weapon fighting.
You can wear Full Plate, and have a Tower Shield, and still be able to use unarmed strikes, two weapon fighting, and Style feats.
Some style feats may have specific restrictions listed within the feat description.