I don't think in the basic install you can just press a button and have the points move. You might export your dbf to a new one, add it back in and use the Add XY Data.
You might, depending on your work flow, add a temporary point using the Sketch tool - right click - Absolute XY, and then move your target point to it using snap, or if it is a new point attribute it after adding it, and then when you are done delete the unattributed points and run the Add XY Coordinates tool to update the table.