Normally, those tiny switches have a pair of contacts.. one for "break" and the other for "make" when the button is pushed. Or two "make" contacts. Only one pair of contacts may be used, but the combo switch can be used with many circuit designs.
It is not practical to use a soldering iron on only one contact at a time to remove it. Minimally, an iron with a broad tip that can breach both side contacts at the same time to allow it to be removed should be used. A plastic 'wedge' pushed under the center of the switch will help lift it when the solder joints melt.
If you have two identical solder irons, and a friend, then one person can induce the device to lift while the other applies the heat. But don't apply heat too long, or damage to other components can result! "Get in and get out" with the heat is the rule.
F@H.. to solve mankind's maladies.. in our lifetimes!