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There is frequently the suggestion to use tighter lens hoods than specified for some lenses when they are used with smaller sensors than they are designed for. The idea is that the vignetting introduced does not matter with the smaller imaging circle.
Now a constriction in front of a lens can and has been used as an external aperture stop. Is there a risk of unintentionally lowering your aperture by using a too-tight lens hood?
For each imaged object point in focus, you have a (double) cone from the entrance pupil running through that object point (where both cones meet and have their tip) and onwards, covering all points in 3D that could have an impact on the image if not occluded.
These cones must not intersect with the lens hood. If they do fully (black vignette) or partly (light reduction), you are changing the image. If the imaged object points form a smaller rectangle (due to the sensor covering a smaller rectangle), the cones will not spread out as far but will start from the same entrance pupil.
A significantly different lens hood only makes sense when the object image spread (where the tips of the cones are) is significant compared to the entrance pupil size. That will mostly happen if we are talking about wide angle lenses. Those have a comparatively small entrance pupil meaning that you'll get hard vignetting rather fast. However, hooding tends to work only so-so for wide angles anyway.
Takeaway: I'd probably not bother.
Vignetting is an aperture effect, visible in the corners more than in the center.
As the limiting border of the lens hood is some centimeters in front of the lens, its effect isn't distributed evenly across the whole picture area, but instead more prominent in the corners.
So before the hood gets a real impact on the overall exposure, you'll clearly see a vignetting.
Some years ago, when I was experimenting with various special lenses and hoods for my SLR, I built a cardbox adapter simulating my SLR body (correct flange focal distance) with a cutout equaling the 24 by 36 mm film size. If, when looking from the "film layer" into the lens, I couldn't see any part of the lens hood, vignetting couldn't be a problem.
Starting with the extreme: home-made bokeh-shape-changer-apparatus.
As can be seen in the example, the metering after placing the paper over the lens was f/3.2, even though the f/1.8 lens was wide open.
So, if we take the lens hood down to an extremely small hole, not only does it become a sort of aperture but it can also change the shape of the bokeh.
On the other side of the test, we'd have a lens hood that is just barely too big - which would cause vignetting. Now, the real question is: at what point would the hood go from causing vignetting to acting more like an aperture? To that, I'm not sure.
