My dog is getting neutered soon. How safe is such an operation? My Vet says it's major surgery and I know that?

some animals can bleed to death, some get serious infections that can lead to death, and some don't wake up after anesthesia because it makes their heart stop and it can't successfully be restarted. So I'm wondering, considering the risks versus the benefits, should I go through with it? The Vet says the risk of a dog getting testicular cancer if it's not neutered is less than 1 %. This is all so scary and I am rethinking this whole neuter spay thing.