Ambient Light cancellation on Pulse Oximeter
What you have presented here, as far as I understand, is a basic calibration problem. Definitely, you will have to make some form of subtraction or compensation for the offset created by that ambient light.
I would run the following algorithm every time the device starts up.
Begin:

Obtain the value of frequency for ambient light conditions i.e. without any excitation from IR or red light. Store this as f_amb.
Loop (RED 10ms, IR 10ms):

Obtain the value of frequency for excitation conditions. Let it be f_ext.

f_actual = f_ext-f_amb

Do pulse oximetry calculations
End Loop


End
The point to note here is that there is no need to incorporate an off time between the 10ms cycles. Instead, just allot a time delay of say 20ms in the device start up sequence for the calibration run. This way, you save a lot of time that would otherwise have gone wasted. This will however be at the cost of reliability because in the case of a change in ambient light conditions, unless the device shuts down and starts up again, you will be getting wrong values. You can add a 'check' sequence for detecting ambient condition changes every few minutes.
All the best!