Ape quest exists in demo and full game on the european PS store (it's the only psp demo for a european account). There are other ones for american accounts.
Sadly you can't just search 'psp demo' on the store, you have to know the exact title beforehand. Or just buy a cheap mini game as the less storage it uses the better for such a hack.
To be on the safe side, install the psp demo or mini game and do a qcma backup on your PC (we don't know how long we'll be able to download from the store with HENkaku).