I did exactly this in February. I went with others, did the stay/play/dine package, so we had hotel, 5 day hoppers and dining plan all packaged together. I went to guest relations in a park to upgrade my ticket. I just had to pay the difference between the AP and the current gate price of the 5 day park hopper. Upon suggestion from a cast member, I waited until the last day of our trip, meaning my new AP started the day I got it, not the day I first used my ticket. That just means it will last 5 days longer. This of course wouldn't benefit you if you need the AP for dining, shopping and parking discounts during your stay.
Don't forget, you need to bring photo ID with you.