I replaced my heater core a short time ago using a short newsletter article that soemone here pointed at as a guide.
No, you don't have to remove the whole dashboard, and you don't have to cut it up with a sawsall to change the heater core.
It does help it you have one or two buddies to help you. If you can find a couple of people to help you, it can probably be done in less than 1 hour.
Basically all you have to do is disconnect the battery, then disconnect the heater core inlet and outlet hoses. Go ahead and cut them off, because you are going to use new hoses. ALWAYS CAREFULLY SCORE AND PEAL AWAY THE HEATER CORE HOSES. OTHERWISE YOU CAN DAMAGE THE HEAT CORE INLET AND OUTLET TUBES AND YOU END UP DOING THIS PROCEDURE AGAIN. Now, remove the linkage that is in the way of the heater core access cover. Remove the heater core access cover. Remove the dashboard side trim panels with the doors open, remove the trim cover from the top of the dashboard. At this point, your two helpers will support the dashboard until you are reassembling the car. Loosen the two top dashboard bolts, and then remove the side dashboard bolts. Now remove the two dashboard top bolts.
Have your helpers lift the dashboard away from it's mounted position far enough for you to pull the heater core out. Swap the seals from the old heater core, and install the new heater core. Help your friends reposition the dashboard to where it belongs, and reinstall all of the dashboard bolts.