It isn't cash? I thought anyone can cash it so if you found it on the street its like having a check addressed to cash. If I did win the lotto and there was no way to send the money back other than mail, yes I would mail it to myself. I am not saying mail is 100%, but 99.9% reliable. I would also choose the better way within reason, If the convenience outweighed the risk I would do mail. For example I win the lotto of 10k but if I want to 100% it, I would have to fly up and spend 2,000$ on tickets and luggage. Or send that in the mail with tracking. I would choose the mail.
If you can issue a stop-payment on a cashier's check before it's cashed, you can prevent the theft. After it's cashed, the only way it won't be honored by the issuing bank is if it was altered.
Cashier's checks are made out to a specific party, usually a company with your account number and so on. Finding that on the street would require you to have credentials proving you are the named payee, or you'd have to alter the check to add your name.
If you're stupid enough to put your real name on an altered cashier's check, you're taking a huge
gamble!

A money order, however, IS similar to cash as long as you left the name field blank when you lost it, or if you filled in the name of the scammer (fake-ID-holding scammer).
But, as with bank checks/cashier's checks, a money order can be canceled if you call customer service and verify it has not been cashed. You can expect to wait up to 8 weeks for a refund or newly issued money order (your choice). You will also be charged a cancellation fee.
it really is important to understand what types of financial instruments exist and how they work -- not only in the majority of cases, but also in "what if" cases like theft, scams, lost instruments or just wanting to cancel. Many of these services are available online, just like paypal.
Yes, these services can charge a fee, but so does PayPal -- unless you're a cheap, lowlife, no-integrity bastard who chooses to lie to PayPal about the nature of the transaction, thereby committing fraud, violating the terms of service, and bypassing the very fraud protections for which most people choose to use PayPal.