Because I was planning to offer shutter tester DIY kits, I built a few prototypes myself, so I can speak from experience. One, you should use an infrared sensor on one side and an infrared diode on the other. Using random light sources for the light to illuminate the sensor yields inconsistent results. The good news is that many devices (like scanners, copiers) employ optical moment limit sensors, which are basically a photo diode and a LED, in most cases, infrared. Many of them can be separated in two by just cutting it, and many have mounting holes which then can be used to easily mount them on a stand. The more difficult part is what you use to measure the time, you really should be using a Schmitt trigger circuit, otherwise the measurement will be imprecise, especially for the high speeds.
The other part to consider is that for lens shutters, the real exposure time is not easy to measure, as during the time the shutter takes to open and then to close the amount of light passing through varies and it adds to the light passing through when the shutter is open fully. The mechanical shutters were adjusted to take that into account, so it may seem like then run slightly slow if you just measure the time the center of the shutter stays open.