I've got a similar trip planned in August --- my confirm from AS for the AS-issued ticket (with the first segment on DL) says that "Alaska Airlines rules and fees apply for this itinerary" --- which in my mind means that I'll be getting a refund from AS for the DL bag fees that get charged (if they in fact get charged).

Take a look at your e-ticket confirm and see if similar language exists under the "Baggage" section (at the very bottom of the confirmation email).

I've got mine printed out.