Denali terrain and shoes

Going to Denali next week for camping and day hikes, yay! I'd planned to just bring normal running shoes that I wear for Cascade hikes but wanted to check that I won't be slogging through mud, in which case I (might) bring heavy water proof boots. Weather says partly cloudy with chance of showers pretty much the entire month of June. Trying to pack light as we have to fit everything in carry-ons + one luggage.