It is easier to just remove the heater box in my opinion. If the core hasn't been replaced, or the foam seals, good time to take care of that.
+2!
Note that there is a long screw that attaches a bracket on the heater to the under-dash. It is easy to miss this screw and tug hard on the box and break off part of the box. Looking from the floor up under the dash, this screw and bracket are just above the vent door.
When reinstalling the box, I like to connect the hoses and clamps to the new heater core first. Position the box on the floor under the dash. Feed the two hoses through the firewall from inside the car. Have someone under the hood pull the hoses through the firewall while you lift the box up into place. This prevents the hoses from folding over and kinking between the box and the firewall. The hoses will want to kink every time and you can't see it. Once the box is up in place and the four studs are through the firewall, attach the nuts to the studs and re-attach the bracket to the under dash. Make sure the wires from the motor have been pulled through the firewall also before tightening the nuts.
Last thought is the original cardboard plenums that lead off the box to the two defroster vent hoses are getting hard to find and seem to be in demand. If you have your original cardboard plenum and defroster vent hoses, treat gently.
Be patient, go slow and good luck with the project.
Jeff