It might work twice, or maybe three times, but those presses get really sticky with the released oils & it gets harder to get your hash out each time, more of it sticks to the inside of the press each time. I had one that was space case branded, but looks exactly the same design, the inserts were hard black plastic in mine, but I don't think that makes much difference. Maybe you could clean it, but they're just not worth the hassle, there are better ways.
I'd use cellophane sandwich bags (the crinkly cellophane bags, not plastic or the hash will stick too much), put some hash in a corner of the bag, twist it tightly around the hash, then wrap it again & keep doing that 4 or 5 times so there are a few layers & it wont split under any pressure. Then apply some pressure, I found using a door was easiest, but you could be creative, if you have some hardback books you don't mind destroying then you can put it between those & stamp on it or something. If it needed some heat then I'd put the wrapped hash in a cup & pour boiling water on it, but good hash will press well without heat. You do need to wrap it securely with a good few layers. You need more layers if it's particularly thin cellophane.
I'd be wary of paper too, but cellophane doesn't stick to hash badly.
