It will be tricky to make wxGenericGrid responsive to cursor key movement, because at present the wxText item always has the focus (in editable mode) and absorbs cursor key presses.
One possible solution is not to have the focus always set on the wxText item. When the user clicks on a cell, the focus is on the cell. When the user presses Return or double-clicks, the focus is set to the wxItem and text may be typed in. Immediately after the user has single-clicked on a cell, cursor keys can be used to navigate around the grid.
In non-editable mode, focus is always on the current cell, and therefore all cursor movements are immediately interpreted as navigation requests.