Yes you can usually get a cashier's check from any bank even when you do not have a checking or savings account with them.
However some banks may only issue cashier's checks to people who have a checking or savings account with them but most banks will still sell you a cashier's check as long as you have the money to pay for the cashier's check and the fee.
The cashier's check fee will vary between banks but most are between $10.00 to $15.00 depending on the amount the cashier's check is being written for.
A good thing about a cashier's check is also that if someone else doesn't have a bank account the person can usually take the cashier's check to the issuing bank and cash it without need for a bank account.