1968 is the stainless steel blade, with the dull finish, since starting with 1967, the government was mandating that finishes through the windshield that could cause glare, be removed.
If the wiper arms are side specific on many of the cars, however, without checking the parts manuals, I can't say what they are on the 1968 Cadillac. There are also very specific instructions on how to mount the wiper arms on the wiper transmission shafts, so they don't "tangle". If those instructions aren't followed exactly, the wiper arms might travel too far to the outside, or might not park properly. Another issue might be that the bronze bushing on the transmission shafts might be either loose or worn, causing problems. Lastly, the wiper motor assembly might have loose or worn parts internally, that can cause similar problems. Everything in the wiper system must work in harmony, if they are to work the way that they did when the car was new. It will be up to you to determine exactly where the problem exists, and this will be a relatively easy task, if you have an original 1968 Cadillac service manual.
Without the manual, you can check for looseness by shutting off the ignition when the wipers arms are at the 12 o'clock position, and lifting the wiper off the windshield and trying to move it to the right and left, and observe the opposite wiper to see if it moves also. If it doesn't, that would be an indication that further investigation into the linkage will be necessary to determine if there are worn parts. If you are unable to move it at all, that would indicate that everything is tight on that side. Then do the same thing on the other side, and compare the results. If they are the same, there is a good chance that the transmission linkages are not worn.