I have a US bank account and the other person in a south Asian country does not.
What are the fees involved?
Both would take the same time. They have to physically be sent to the Bank in US by the Bank in Asia. Generally for individuals it would take around 3-6 weeks for funds to be credited
There would be no fees to you. The bank in Asia may charge the beneficiary around 10 to 30 USD, varies from bank to bank and country you are interested.
You trivially use ofx.com or transferwise.com. (Or any such competitor service, all of which are huge multinational businesses.)
Using a cheque is all of incredibly slow, very complicated, and has astoundingly high fees, and you will be gouged senseless on the rate. It's just a non-starter.
(In answer to your actual question - the "cashier's cheque" is probably >slower< if anything. But it's irrelevant.)
In contrast it is 2 clicks to do this using one of the many services which, obviously, exist for this purpose. It will take you maybe 5 minutes.
If you think about it for a minute, about 1 zillion times a day money needs to be moved from country A to country B. Just do it the normal way.