It will depend on 2 factors:

1. Whether seats are available in the next class of service, and
2. The type of ticket you have

If Expedia and Delta are telling you that you can't upgrade your ticket than it's probably because you are on a discount fare. If that is the case then you won't be able to upgrade your tickets at the airport. As you have been advised, the only way is to cancel them (and you might not get anything back) and buy new tickets in Business Class. Your call, but it might not be worth it.

Why not see how it works out on the outbound and, if it is as bad as you fear, you can judge whether to pay for the 1-way Business fare on the return?

Whatever you decide, good luck with it.