I would definitely not let mine have the vaccine at the same time as the surgery. Too much on her little body at once. Besides, you want to know if something you are seeing is the result of the surgery and pain meds, or the vaccine.
There is a combo shot available that does not contain the lepto & corona portion, I'm surprised that your vet does not carry both.
If you take your dog to a groomer or board them, then they will probably require proof of these vaccines. If you do your grooming yourself and never board, then there is no law that forces you to get vaccines other than rabies. Whether you think the risk of not getting the vaccines is worth it is up to you.
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