Is there a kind of switch that after being pressed, even if not released, will open the circuit again?
One option is to use a magnet (on the door) and reed switch (on the frame) and mount the reed switch slightly back from the fully open position. In normal use the reed will pulse just before the door is fully opened and will turn off when actually fully open. You will still have the original problem if the door is stopped on the reed switch.

Depending on the orientation of the switch in your photo, you may be able to design a bump-cam to press the switch as it passes.

NO / NC switch combination







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Combination of two microswitches to give momentary pulse as door opens or closes.

A third option is to use a pair of the type of micro-switches you have already used. 


Wire the switches in series as an NO and NC pair. (I've shown single-throw switches for clarity. You will use the appropriate contacts of the changeover micro switches.)
Bend the SW1 roller out so that it makes a little before SW2 breaks.
You should hear a double-click as the door is opened.




Figure 2. @Andrea's (the OP) implementation of the idea. Switches appear to be rotated to effect the make-before-break sequence rather than bend the lever as I suggested. Hi-res image here.