Yeah, so that doesn't make sense. If you've received an award (let's say a NAM), you've received a 1650 and/or citation. No one is going to put CLASS info in the award, but the award itself is still issued. If it's a unit award, there should be a PAGE 13 for the award, and if there isn't, you should get one. Yes, there are messages issuing awards to commands for unit citations (campaign awards), but sometimes they are hard to get your hands on. So lacking that, get a page 13. And if you're not in the command to get those, your current command can still write a PG 13 based on your time of service and issued unit award.
So all that said, to answer your original question:
Wear what you have documentation for. Bottom line, NDAWS isn't the end-all of documentation.