Whatever happens here is "on DL", it is up tp them to fix it.
By law all DL must do is refund your cash if you can not fly (does not matter when you elect to not show or cancel).
In practice, DL is fairly good about offering you a choice on other flights that are about the same as what you bought.
Best solution is to decide what is best for you. If you want to make the trip, and DL has a flight that works, call and ask for that. If you would rather just throw in the towel, ask for the money back.
No need to worry about the departure time of the re-scheduled flight, that was DL's bad.