I really won’t recommend putting any source of vibration on the scope. Even tho the effect, depending on the fan, might be negligible, it just should be avoided out of principle. Raspberry Pi 4 overheats without cooling and adjusts clock, yes, but performance is still better than with Pi 3. I guess for basic operation of the microscope, the performance of the Pi 3 should be sufficient and if it isn’t I would say there is rather a problem with the software.
Depending on the type of operation, a scope might have a lot of uptime and so would the fan. Cheap as fans wear out quick and you get even more vibrations. So you end up with with a part which has to be serviced and in the current housing stack, this takes some time. So what would be a economic solution in that case? Well, I would buy at least the best fan there is, which has minimal vibrations and runs virtually forever without any degradation. Just sets you back 13€.
What else do we get for 13€? Passive cooling for the Raspberry 4! 
So if I would run into the problem of overheating I would design a housing with more air convection. The current one is rather tight in that regard. And modify the board mount so it supports an available passive heat sink.
If a version using such a heat sink would become the recommended design version of the Scope, someone may argue that this takes away some openness, or at least, we need a rather propriety part to build it, compared to a standard 40mm fan and a 3D printed mount. However, I guess that’s just the issue of using a non-open board like Raspberry Pi in the first place. There are many applications where someone would use a Raspberry Pi, but where a fan is just not possible. So I suspect that these passive cooling heat sinks for the Pi will get quasi-standard and as available as the Pi itself.