If you can get the potato head someplace else, take it with you to Disneyland, but do not take it to the store. Pack all the necessary parts and the other accessories in the box. There are heads at the store, too, so you can try on the accessories on those heads, but you do not have to buy them.
If you do end up getting the head, open the compartment, and fit what you can inside, then whatever else you can around the head. Whatever you fit in the box and still close the lid is what you get to take with you.
Note - even if you have hands, get the ones at DCA because they can "grasp" the accessories like the Mickey glove, Mickey ice cream bar, etc. Things I remember them having: Goofy hat, Mickey hat, Mickey's sorcerer hat, Mickey groom hat, Mickey bride hat, Mickey balloon, glove, and ice cream bar. Minnies shoes...
They also sell "kits" that have the Potato head & accessories all together, however, you do not get as many parts. You can see these at the back of the store in the pic I posted, and you can see some samples of of Mr. Potato Head on top.
There is no time limit to get all this stuff. When we went, the store was kind of empty, so my SIL had a lot of time - she spent probably a half hour in there. If the store is crowded, however, I would imagine your time would be limited by the people who are waiting.