The timer would not need to be onboard the spinning flywheel, it could be on an observing quasite orbiting higher. When it's time to launch it could shine a control laser at the flywheel, which is used to time the triggering of a cutting laser at the right position to slice the payload off at the correct angle.
One timer could be used to launch multiple flywheel payloads over time
One timer could be used to launch multiple flywheel payloads over time