I don't think it has anything to do with the SkyMiles account. Everytime I price tickets from CPH, the fare is quoted in DKK. This happens whether I log in or not. And it showed that way even when my SkyMiles account was resident in the US.

Indeed, if you price a DL itinerary ex-CPH on ITA and look at the fare construction details, the fare is shown in DKK. So, I think it is pretty clear that DL only sets prices for ex-CPH itineraries in DKK. Even if they were to show you the USD price on the website, the underlying price would be in DKK.