If your vets are telling you she needs surgery, then maybe you should have it done. I was a vet tech for 8 years. Dogs that are not elderly take the anesthesia well, and wake up from it in a couple of hours. She may need a collar (lampshade style) to keep her from licking the area. But it does not sound like a bad idea to me. Blessings - Blu
If she is not spay, and due to her age, there is a higher chance she "could" get cancer.
No matter the age, if I see or feel a suspicious lump, I at least have an aspiration biopsy done.
I felt a very small lump in our Greyhound's throat (couldn't see it yet). Took him right into the Vet and had it aspirated. He had Lymphoma.
I am glad you noticed these and are seeking advice. It is a good idea for every pet owner to go over their dogs to check for anything that might be suspicious.
If the Vet thinks she is in good enough health to be spay, I would have it all done at the same time. But, make sure she is checked out well physically and a full blood panel is done before any surgery.
I also noticed, very, very small lumps on my little girl's belly, smaller than yours, also only to be felt by hand, and not seen. I went to the doctor and they said it is probably nothing, but let's get them out anyway, to avoid future risks. It turned out it was melanoma malignant... I don't want to alarm you, it could go either way, but you should check them out...