I guess one question is, to what end? To see if the shutter is running mechanically slow or hanging up? The electronic timing of the shutter is likely to be as reliable or better than one's test instrument.
If there is some reason to test it or just curiosity, and the main problem you face is lack of access to the back side of the shutter, and the camera has a mechanical shutter (many digital cameras no longer have a shutter) ... it may be possible to test the shutter by measuring the reflectance change off the sensor vs the shutter blades. Sensors tend to have a moderately reflective cover glass while shutter blades are dark. If it's a DSLR and you can't lock the mirror up, you could probably black out the focusing screen so that image is dark as well, so the mirror and shutter are dark-ish and your detector measures an increase in reflectance when the camera sensor is exposed. Clearly this would have to be homebrewed with perhaps: a light source, some photodiodes (with maybe a snoot or optics so they each "see" part of the sensor), and a storage oscilloscope.