Fixing the program button on a Phonak Bolero B SP

So today I took the plunge: My left HA’s program button stopped functioning a week ago, so I want to open and clean her up.

I took out the three pins and disassembled the HA:

(Take care with the pins, because they are tiny and I spent 10m searching for one that got swept to the floor.)

The button is wedged into a plastic, silicon-like element, that also covers the two microphones:

After removing that piece of plastic, the button between the microphones looks like this:

The problem became apparent when I pressed the button: the parts of the button are loose. It is composed of two metallic plates and a small round element on a piece of sticky tape:

My first idea is to replace the piece of sticky tape with one with another round element in the midlle, so that everything is held together again. It works for now, but I do not know whether it is the good approach.

Is there anybody with experience that could point me in the direction of a proper way to fix this? I am not thrilled about replacing the switch, because the surface mounted device (SMD switch) is tiny and I rather do a quick fix, than damage the HA.