Do shapes connote differing degrees of hazard?

I'm working on designing an icon set and experimenting with a few different styles. One style would involve every icon being the same color. However, color is really good at differentiating things like a soft warning (yellow) and a more urgent warning (red).

I wanted to experiment with the idea of using shapes to convey different degrees of hazard. The audience for the project will likely stay in the States, so I don't think I need to anticipate Eastern vs. Western clashes or that sort of thing. Consider the following (really basic) example:

My perception of shapes is informed by road signs, so I personally feel like the diamond and triangle shapes feel more "alert"-like. The octagon obviously says stop, but it's not very distinct from the circle. The circle feels softer than the square, but that's about it.

Semiotics is not my field, so this link about general research didn't mean a whole lot to me. This question about traffic light shapes was an interesting find, but I don't know how universal it is (I'd never seen anything like that before).

So, do basic polygons carry hazardous connotations (or any other connotation, really)? If so, what's the basis...anything other than road signs?