Any surgery is hard on chihuahuas. Has your vet recommended this surgery? Has the vet/groomer told you that the anal glands are 'impacted/full? It may be that the gland/s just have to be expressed. Not something I'm comfortable doing. Some dogs have problems with their glands, and others go their whole lives with out trouble.
I've had a chihuahua that actually had a ruptured anal gland that had abcessed. What a mess! Sitz baths for a dog!