Pega doesn't provide when on button control action set, you can change the control to formatted text with label inside <a>label</a> to look like link so that you will get the when rule on each action. With button its not possible.
I believe "Run Activity" action would not solve your purpose, because it doesn't send any response back to client. It is just used to execute an activity at server side and to manipulate the clipboard pages. Instead Refresh Section would be a best fit to run some activity / data transfrom and to bring the response back from server.