I'm assuming this is a factory A/C unit?
You should remove the COMPLETE heater/AC unit as unit. When it is out of the car then open the fiberglass casing. The 2 halves (upper & lower) are held together with spring clips. This will expose the heater core & evaporator, plus the various 'doors' & seals inside the box.
First step is to remove the 2 'pie plates' where the heater lines & freon lines protrude through the firewall.
Second step is to remove the passenger seat (you'll need the room).
Third- disconnect the vacuum lines & electrical connectors.
The entire unit is secured in the car by studs through the firewall and another fastener up by the cowl fresh air inlet. Be very careful in the removal. The studs on the fiberglass housing can be broken. IIRC, the mating of the unit to the blower motor is just a slip joint.
This is NOT a fun job. Be patient and go slow.
Be SURE to pressure check the new heater core prior to installing. (Ask me how I know)

I've never found a bad evaporator in '67 or '68. Flushing with an A/C cleaning solvent should do the trick. But as long as you have access- leak check it as well.
Installing the completed unit is a PITA- lining up all the studs through the firewall and securing the fastener at the Fresh Air inlet requires a helper.
I converted my CS to a rotary compressor & R134 freon, with a new expansion valve & oversized Condensor + hoses from ACC. It blows out 40 degree air.

Hope all this helps. If you need me: 828-507=2530 cell
Neil
PS: I forgot to mention- remove the glove box for easier access,