Is there a secret in getting off the windshield wiper arm from the
spindle on a 1968 Olds Cutlass S?

 

not sure if 67 and 68 are the same but try this link

https://classicoldsmobile.com/forums...r-removal.html

 

Does anyone know if there is a spring clip for a 1968, similar to the 1967 which is mentioned?

 

Sometimes they need a little persuasion. A few light taps on the top with a hard rubber mallet while holding pressure/tension from below while pulling on spring clip to release and voila. However they are "clocked" and will need to go back on just like they came off.