CO would allow BusinessFirst passengers to have access to the club in HNL for travel, but in the UA world, not sure what the policy is.

But if you're connecting from a Hawaiian Airline in first class, you can also hang out in the Hawaiian Air lounge just by showing your HA F boarding pass. I'll hang out in the one that's upstairs near the WikiWiki stop, and then just take the WikiWiki over to the UA gates when you're ready to go. Snacks are more limited than UA's offerings, but you can stock up on guava juice and Kona coffee and their snack mix and relax while Hawaiian music is piped-in in comfortable surroundings.

The lounge by the interisland gates on the main level is larger, but it's less convenient to get over to the mainland departure gates.