Spring-Loading the flap is easy.
But what holds the Shotgun in place ?
I put one of these behind our bedroom door - In-Wall Security Cabinet – 55" - Stack-On
It took all of about 20 minutes to install with a drywall saw and drill/driver.
It is discrete (you have to be in the bedroom and close the door to see it), allows quick access to a shotgun, and keeps it secure from little hands.
(As an added benefit it also opened up two spots in the safe.....lol)