And that's the tricky part: even a signed message from the address that funded the wallet doesn't necessarily mean it's the ownerr (it could be the guy who sold the Bitcoins to the current owner).
If you buy or get a paper wallet from someone you can't 100% trust for the lifetime of the paper wallet, you should move the coins off the paper wallet and create your own one as destination if you want to keep a paper wallet.
Another way to get the owners attention could be by leaving small hints by sending dust to the address and in the same transaction sending dust to for instance those 2 addresses:
1PaperWaLLetFound1xxxxxxxxy1KHknm
1Topic54o8263onBitcointaLkxyvdAVg
(Note: I used Proof of Burn to create those addresses. DO NOT send anything valuable to those addresses, it will be lost forever).The owner will have to know his address, but if he knows it and the wallet was indeed stolen, it's not unlikely they'll check a block explorer to see if the funds were moved. When they do, they'll see the new transaction with hints.
While easier to spot with such "burn addresses" unfortunately this bloats the UTXO set.
An OP_RETURN "Found lost or stolen paper wallet, see thread on bitcointalk.org" as transaction output at the proper place speaks for itself, but frankly isn't for newbies. Sorry, I don't want to derail this thread.
IF they still have the private key, they should just move the funds the moment they realize a copy is missing.
That should happen likely but would leave @easternklaas as apparently honest finder with empty pockets unless the legit owner shows some gratitude to the honest finder.