The word "shut" is used many different ways. The right sign for "shut" depends on what you mean.
If you mean "shut" as in "shut down," or "shut off" then use the "power off" sign. Start with your fingers spread and then lower your arms just a bit while bringing your fingers and thumb together (into flattened "O" shapes).
POWER OFF / shut off / shut down / headlights off / power down a computer /
If you mean "shut" as in "shut the door," use the DOOR-close sign
DOOR-close / "shut the door":
If you mean "shut" as in "shut-off the over-head lighting" then use the "lights off" sign.
LIGHTS-OFF:
If you mean "shut" as in "the light shut off" or "turn it off" you can do a very general, very casual version of "shut-off."
SHUT OFF:
If you mean "shut" as in "shut up" or "quit talking" see: "SHUT-UP"
Notes:
There are dozens of other ways to sign shut: "shut a book," "shut a drawer," "shut off your voice," "shut your eyes," etc.
Notes: