When my little conure was ill, I had to take him to a different vet because my vet was closed. They were not used to birds and wanted to sedate him for bloodwork, and I also said no. They wanted me to sign a paper that said that he may not wake up and I was like, nope.
My vet was in several days later and took blood right from his neck while she was holding him. He wasn't stressed at all by her doing it that way. He was also smaller than a cockatiel.
Did the vet you're going to tell you that about sedation?
I want to mention that the vet who didn't know what she was doing ended up taking blood from one of his toenails, but she didn't clean his foot first and the test came back completely contaminated. If they end up taking it from a toenail, make sure that they clean his foot first
If you're in the US, it looks like this company could do the tests with blood taken in different ways.
IQ Bird Testing
I'm not in the US but hopefully someone knows whether this lab is reliable.