Update - I managed to find (from online discussions) a shape moving feature under VIEW -> Add-Ons -> Visio Extras -> Move Shapes.


A popup will come out, which has default numbers in the entry boxes. Here, I have to set those non-zero values to ZERO. And then I set (for example) the horizontal value to -0.01 or +0.01 mm (which will be the stepping size) ..... I put a + or - sign depending on which direction I want to make the shape move when the 'apply' button is used. The shape will then jump in steps of that given increment every time I hit the 'apply' button.



Also - naturally, before we hit the 'apply' button, we have to use the mouse to select the shape we want to move.


We can also ZOOM in very close - such as 500% zoom - so that we can get a good view of the shape's edge as we do the fine jumps. And - if the selection box outline hampers our view. We can also keep jumping and 'overstep' the mark. And then we can always de-select the shape (which then removes selection outlines) ------ and use the CTRL-Z (undo) key combination to keep undoing the steps.