1) Is the duty cycle intended to be a constant 20% before you press the switch?
2) Can you monitor duty cycle on the scope before you press the switch?
3) Can you capture the scope waveform exactly 350ms after pressing the switch?
4) With a 100Hz PWM frequency there will be only 35 pulses in that 350ms period, so the RC filter method probably won't work ;(
The duty cycle is 20% before the switch and I have measured the same.
capturing exactly 350ms after the switch is tricky. Can be done by feeding the switch input to the second channel and matching it.
Read those pages, your scope should be able to do it, set the width on scope to 70% and trigger on button press (use external trigger?), your scope is capable of pre capture.