Child safe flic
This is a suggestion for a product improvement.
The BATTERY in the flic is DANGEROUS to children.
It is relatively easy for a child to open up the flic and swallow the battery or the lid. The base sticks fairly well, and can be glued, still - the entire button looks delicious and may be eaten as well.
One solution may be to make it possible to "lock" the flic together by a small optional screw.
There are naturally several other ways that could be employed in any future design. Maybe even a separate "child safe flic". The current delicious, easy to pick apart design is absolutely fabulous, and we might be able to make it safer for children in the future.
In the meantime consider glueing the two parts of the button together with a strong (but removable) adhesive.
As a solvent I suggest using either Isopropyl Alcohol (that's the alcohol in rubbing wipes) or Acetone. When using the latter you may want to wear some 1-way cleaning gloves because prolonged exposure to Acetone isn't super nice to the fingers. This being said I know chemists who don't care and just handle it like water.
You could also use hot glue the button to the wall and then to remove it use heat (and / or also the solvents mentioned above). However heat and electronics don't go that well together normally, so do that with caution.
Out of all these options I'd go with Isopropyl (Isopropanol – same thing) alcohol. That stuff is generally safe for electronics and in fact used to clean up solder spots on PCBs.
Hope this helps!