You can do this at runtime, but it's not easy: to make the code robust you need to parse the vertex declaration to find out the location and format of the position field, then extract the relevant sequence of bytes and convert them from whatever format they are in (this will often be a Vector3, but could be other formats as well), and you also need to take account of the index data. The GPU mesh format is optimized for rendering, and not particularly easy to work with on the CPU side.
Why can't you use a content processor for this? It is much easier that way!
Alternatively, I wonder whether you even need to do a true mesh hit test to implement a gizmo? That seems like a simple enough shape that you could just do 2D geometric tests: check if the point is inside the central circle, test whether it is within a specified distance of one of the axis lines, etc. The nice thing about doing that is that you can tweak the hit-test tolerances differently to the visual appearance: to make a gizmo feel good, you might want the axis lines to have a slightly wider hit region than how they are rendered, for instance.
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