Perhaps add something small and skinny, and sticky (such as a small pice of double stick tape between the sliding plastic piece and the base of time mouse? It will have the effect of making it harder to turn on the mouse, but may solve your problem. Only other thing that comes to mind is using a piece of scotch or similar tape to (semi)permanently attach the power trigger button to the inside base of the mouse. Up to you how strong you want to go with the adhesives of course!
-Mike