If I get a cashiers check from my bank but decide not to use it, would my bank give me a refund for it?
In my experience, if you take an unused cashier's check that was drawn from your bank account back to the bank you got it from, they will cancel the cashier's check and issue a refund back to your account.
I've never had a situation where I cannot cancel a cashiers check from the institution that issued it if I'm the one who ordered it. YMMV, call the institution and ask if there is a procedure you need to follow, or if they will just cancel it for you (or if they won't).
You will not receive a refund for any processing fee by policy, but it never hurts to ask.
Real world data point: I've done it. There was a bit of a delay because I wanted it reissued for a slightly smaller amount and there wasn't enough money in the account to issue the new one without refunding the first one and I was not at the branch I had originally gotten it from. Half an hour later I had my new check.