I once had to put a parakeet down, rat had gotten a hold of it and done severe damage. I just held the little guy really tight in my hands until he was no longer breathing. It didn't take much and it was over quickly. I wouldn't want to freeze something, I'm afraid ether would burn too long in the lungs, chopping the head off...ummm, not too bad, but could be messy. Drowning doesn't take long, it is quick and pretty much painless, just some panic, but that is what I do with skunks and mice.
I had a pet mouse for over 2 and half years that was a very good little mousy, when she got real bad one day I couldn't do any of the above to her. I felt so bad, I kept her warm and took her to the vet clinic where the vet let me put her under heavy sedation until she quit breathing. That poor vet, you shoulda' seen the look he gave me when I asked if he could put my mouse down. Poor guy, I know him because I take care of his horse and we have gone on group rides together. So when I showed up on a Sunday with this little mouse and he was working with some emergencies, he just turned on the gas and had me hold the funnel over my mouse. I took my little mousy home and buried her.
oh yeah, the rat was given to some one with a hungry snake. I just could stand to look at it anymore in the house and it was not a very friendly rat. That was my one and only time trying to own a rat as a pet.