SAS systems are deeply incompetent and check-in is no exception. It is frequently impossible to get a boarding pass for an SAS flight even when checking in at a United counter. So, yes, you need to go to the SAS counter at ORD to get a board pass.
It is clear that the systems for UA and SK don't "speak" to each other well. Often, United agents are also confused by the lack of a boarding pass, so keep your expectations low. On the bright side, SAS long-haul flights have a nice business class set-up, so hopefully your in-flight experience will be better.