No, the fast type change can't be used to replace dimensions too. What you can try instead is create separate chart objects and show/hide them as needed. You can use the conditional display option on the Layout tab for this, for example with an expression that checks the value of a variable or a selected value in a list box.
You can do as suggested by Gysbert or there is one more option explained in Qlikview example documents(comes with Qlikview desktop download). You can check 'Whats new in Qlikview 11' qvw and go to the 'Reports' tab. There is a good way of creating dynamic reports based on user selected dimensions and expressions. I have attached a snapshot of it.
Hope this helps,