Just making sure that the ticket from DTW to SHA was also a delta coded ticket. The ticket number would start with 006.

The fact that the flight is operated by another carrier, doesn't bother me. It's a connection carrier.

But, the thought of losing a first class seat causes me to pause. If they need to rebook me, it may nor may not be in first. They may, or may not, charge me.

If you are ok with the possibility that they may need to rebook you in coach on a later flight if you miss your connecion, take the risk.