Please skip @throws MemoryError. Any object creation can do that, but it is very unlikely because such objects are small. Even trivial getX methods can run out of memory if they return a copy and I don't think it is reasonable to document that everywhere.
Mapping.getInverse makes a deep copy and sets the invert flag on it, and neither of these operations has a known reason to fail, so no @throw notation is called for. That said, it is certainly possible to make Mapping.getInverse throw a runtime_error. It just takes work (e.g. calling AST directly and putting it into an error state) or an astshim bug (forgetting to check for the error state somewhere).
Also I think the note should be reworded for clarity. Any mapping may have a valid forward transform, a valid inverse transform or both. Calling Mapping.getInverse returns a deep copy of the mapping with its internal Invert flag toggled. This maps which internal transform is called by tranForward and tranInverse.
Note that astshim Mapping methods include getTranForward (does the forward transform exists?), getTranInverse (does the inverse transform exist?) and isInverted (is the internal Invert flag set?). You may want to provide access to these, though preferably using a different name for the first two.