Mach 7??
I am not sure the camera lens will survive, some people reported lens error after the camera was dropped from like 30 cm. Either way, if you have access to such a rocket, I guess the cost of the camera is not a problem, so just open the camera and solder the new battery directly on the external power connector. Then to make sure it will stay there, you can glue the battery to the camera with some epoxy or something.
Is there any reason you want to use a Canon camera though? if I were you, i'd use a camera without movable lenses, connected to a PIC/AVR microcontroller.