Yeah, that's the line of thought I was operating on. That if someone was looking for it, they'd automatically go to the police station, and ask whether someone has reported any missing pieces of paper or what not. That's the only reason I automatically jumped to that conclusion. However, I guess individuals in the police force might not be trusted with that kind of information.
There might be one alternative: take it and leave behind a note with your contact information so the original owner can reach out you and pick it up. If this note has the same shape, size and material of the paper wallet, you don't really change the 'situation' at all. It would have the same chance of being destroyed, blown into the sea, stolen, trashed as the original paper wallet.
Probably a decent solution to the predicament. Although, the person may not want to be linked to the wallet, due to privacy issues. Although, I'm playing devil's advocate there. I imagine most people would be grateful that someone went into the effort. Plus, a note could be left which doesn't give too much information away to random people who happen to be passing by. Good solution if you ask me.