About the torque of mini servo motor
You must specify the linear displacement of the switch and required maximum slew rate and thus toggle frequency.

The torque is 2.2kg-cm or 22kg-mm is enough to damage the switch so spring load force is not likely an issue. 

Response time of 120ms is slow for 60 deg. But for 20 deg it may be 40ms or more.  

What is needed to create say 3mm linear displacement in 20 deg rotation at some radius?

One approach is the design of a friction roller Cam on the servo arm.