How big is the light sensor? It should work with caveats for focal plane shutters, as long as the slit opening is larger than the sensor receiving light, if you position the sensor close behind the shutter curtains. "Caveats" meaning you understand the accuracy will be degraded a little, as it will probably read a little slow due to the finite size of the sensor.
I have used a homemade 3mm phototransistor setup (like a homemade Photoplug) with a single sensor to measure focal plane shutter speeds and it works, but I keep in mind that: I'm not concerned with more than 1/3 stop accuracy, and I'm not terribly concerned about the fastest speed. Ideally for a focal plane shutter one wants two sensors to measure curtain travel times and uniformity of exposure, but to first order, I just want to know if the shutter is far out of spec.
My experience using a PWM switched LED bike light as a source, for one of my phototransistors that switches fast enough to resolve the PWM of the LED, is that the PWM switching frequency was over 16-20 kHz. Fast enough that it's not going to matter unless you are trying to measure a 1/8000 sec shutter speed. For a slower phototransistor and possibly some capacitance in the circuit, it would be slow enough to integrate over the PWM anyway (but limit the highest speed that could be measured).