Doing it this way, is it possible to have a button that changes the board and not the set?
Unfortunately not. The third argument is for different-army contexts. If the parameter perArmy=1 is added the pieces of the sets mentioned in the 2nd and 3rd argument are both included, but for the initial setup the piece lines in the white set would ignore the placement of the black pieces, and vice versa. It will then generate two identical rows of buttons, one for selecting the white and one for the black army.
Unfortunately not. The third argument is for different-army contexts. If the parameter perArmy=1 is added the pieces of the sets mentioned in the 2nd and 3rd argument are both included, but for the initial setup the piece lines in the white set would ignore the placement of the black pieces, and vice versa. It will then generate two identical rows of buttons, one for selecting the white and one for the black army.