For lack of a better term, this thing is called the Bad CoonBrand
"Varnax Pivot"

clock stopper The purpose of this gadget is to shut off the alarm as soon as it trips so as not to freak out the chickens.

Solution (1) is the drawing & pictures shown to the right. A pivoted board is kind of complicated, but it seemed like a good idea at the time. If I made another one, I'd use a hinge either in place of the pivot or like Solution (2).

The yellow block is a little board that pivots on a fixed bolt. It's longer and heavier on the left side so it tilts the right side up to hit the alarm button when released. The pivot bolt is the yellow dot, it's 5/16 diameter, anchored in the 2x4. It passes through a short piece of 3/8 copper tube which is glued inside the hole passing through the yellow Varnax board (that'll be a 3/8 inch hole in the Varnax), and used as a bushing together with metal washers on each side of the Varnax board, and a nylon loc-nut. The little red dot on the yellow board is a headless nail which is secured by the 2x2 arm in the left drawing and holds the varnax board in ready position. A wire is attached to the other end, which pokes the alarm button when the trigger is tripped. From the time the alarm goes off, the headless nail is released, and the board flips up to press against the hammer, takes less than a second.

Solution 2

clock stopper

Another alarm button pusher:
(solution #2 --->)
A light weight bungie about 8 or 10 inches long tied to a hinged board. The bungie cord, (maybe an elastic hair tie) acts as a spring, (so it still allows the henhouse door to close when it pulls taunt, it should have just enough tension to pull the alarm button off (i.e. not much).

I haven't made this version, but it seems pretty simple. It's probably not as quick to shut off the alarm as Solution 1, (maybe 2 or 3 seconds) so you might have to dampen the alarm bell somehow so the birds don't get upset.