Most of the keys are the same, so I would contact Whirpool/Maytag, and give the model of the push & slide mechanism, and the washer model.
I know this because my friend works in a Laundrette, and they use just the one key to open all the push mechanism from all machines (there Extra Large capacity machine is the only one that needs a different key, as it contains the more modern single slot, which accepts 20 p & £1 coins as opposed to a push & slide).
You can insert blockers, so that you don't have to insert coins, these blockers stay in place, and if all money slots have a blocker in, pushing it in will start the washer, no coins needed! I think a key is needed to insert the blockers though?
For instance, There 10 slot mechanisms - they Blocked out 2x50p coins slot (2 available), plus one 20p coin clot, and one £1 coin slot, they also blocked out the 1 10p coin slot, as what laundrette uses them these days!!! They charge £2.60 so they left open 3x20p (of the 4 available) slots, 2 x£1 (of the 3 available). They don't deal with 50p coins any more. The larger machines, have 4x£1 slots instead of the 10p slot (at £4.80), and as mentioned above the larger machine is £5.60, but that doesn't have the mechanism.