You can have two charts: one that shows the values on data points and another that does not. Overlay them, and use a variable in the Show/Hide condition (on the layout tab) for each chart. Have the button set the variable to the appropriate value for which chart should show. I'm not sure if there is a way to check or uncheck the box by using a macro, but I'm thinking there isn't...
Actually if you expand the expression list there is an option to enter an expression under the heading "Show Value".
Start by expanding the expression you are working with (as per screen shot) and click on the box marked "show value"
In the definition, enter an expression that evaluates to 1 to show the values and 0 to remove them. This can be a reference to a variable that is set by clicking a button.
One warning though: you need "values on data points" unchecked. If it becomes checked it overrides the expression.