How do I combine predictions from classifiers for two different problem?
My intuition would be to try to integrate the information about the products directly in the original model. Typically the possible products in a shipment can be represented as boolean features (one hot encoding), but this part might need some feature engineering if there are too many different products:

simple option: only a small set of features representing types of products (I'm assuming that it's not the specific product which causes custom delays, it's the type of product)
advanced option: feature selection/extraction to reduce the number of features

Generally a joint model (a single model which deals with all the information at once) tends to perform better, in particular because in the other option errors in the first model propagate to the second one. Also the two models option doesn't allow the second model to leverage any specific feature from the first one.
Note that this is just my intuition, I could be wrong.
Side note: probably this is already taken into account but I guess that the value of the shipment is also an important factor for customs delays.