That should work. Some agents say fare class in F matters but it does not. First is first and they should process the SDC without issues or you may even be able to do it during check-in. The only caveat would be that you can't swap from a connection to a non-stop and usually can't swap from a first class flight to a Delta One flight.

Here is the relevant text form the Delta site:

• If you have a premium cabin fare like Delta OneŽ, Delta Premium Select or First Class you may make a Same-Day Confirmed change as long as a seat is available in the cabin purchased or a lower cabin