Yeah, that's pretty much how to do it without the following the proper service procedure of removing the dash and top cover of the airbox. I'm sure there are threads here on the forum which have photos & step-by-step for both the quick and the proper methods.
I did the cut and replace method myself. I think it was maybe 20 minutes with a dremel. Other people use a utility knife. Whatever tool you use, do not cut anywhere outside of the triangle area or you may put a hole in the heater core.
When you look at the bottom of the plenum on the left side towards the firewall you will see a triangular section with a round nub sticking down in the corner of it. That nub is where the bottom hinge of the door rests. Your best best is to cut starting behind the nub all the way to the opposite side of the triangle. Cut a slot an inch or more wide, but do not cut the nub area free of the airbox! You want to create a flap you can carefully bend down which includes the nub at the end. Pop the actuator off the top of the airbox so you can freely swing the door with you fingers to have it drop through the slot you have created. Simply slide the new door back up through the slot, align the hinge ends in the top hole and the bottom nub. Place the actuator back on top, slowly move the door side to side until it the hinge lines up and the actuator can pop back down. Push your plastic flap closed on the bottom and tape or epoxy back in place. Be careful not to push the flap past flush or the door could hang up on it. Check operation by turning on vehicle and turning temp control from full cold to full hot a few times.
Napa and Oreilly's/Murrays usually stock the HVAC blend door kit (plastic blend door and directional door together) for less than $15. It's Dorman - Heater Blend Door Part Number: 902-202. Quick and cheap assuming you are okay with another plastic door which will last about as long as the OEM original.