The M&P 9c is available with no internal lock, no thumb safety and no magazine safety which is (in my opinion) the best model for a concealed carry gun. All M&Ps come with a trigger safety built-in.
Per S&W: "After firing you must allow the trigger to move forward fully before you can fire another shot. Failure to do so will prevent the lockwork from fully cycling and will prevent your being able to fire the next shot."
I carry my M&P 9c with 11 rounds in the magazine and one in the chamber, ready to fire, in a Desantis OWB holster which covers the trigger completely, preventing it from snagging on my shirt.
Here's the link to the exact model -
Product: Smith & Wesson M&P9c - Compact Size