Hi
The status profile usually works with the SO type like OR, QT, IN, CR, DR etc. there is no option of assigning status profile to Delivery Document types.
The logic is if you want to use approvals you should do it while creating the SO and not in any preceding document through status profiles, because once delivery is created and user does some changes in the SO it will not be reflected in delivery document any way and vice versa.
Now if you want to control the creation of delivery document, you should also consider applying the delivery blocks in the SO.