If you're on a ZED fare they might be more lenient, especially if there's room. I didn't work for DL, but when I was a gate agent, we almost always gave the interline nonrevs more leeway than we would those who worked for the company and knew better. The exceptions were when the bag was clearly too big or the excess went to an extreme.
Worst case, ask the agents and volunteer to check the extra carry-on bag if you get accommodated. You'll get a good indication right then on whether or not they'll be giving you a hard time later by taking an extra.