4 lbs is not too small. I usually spay at 6 months. If you don't trust your vet, you can find one at:
https://www.aaha.org/
It is always good to be sure your vet is accredited.
Information on mammary tumors/cancer:
https://www.acvs.org/small-animal/ma...mmary%20tumors.
From the above link:
"Mammary tumors are more common in female dogs that are either not spayed or were spayed after 2 years of age. The risk of a dog developing a mammary tumor is 0.5% if spayed before their first heat (approximately 6 months of age), 8% after their first heat, and 26% after their second heat. Cats spayed before 6 months of age have a 7-times reduced risk of developing mammary cancer and spaying at any age reduces the risk of mammary tumors by 40% to 60% in cats.
More than a quarter of unspayed female dogs will develop a mammary tumor during their lifetime. The risk is much lower for spayed female dogs, male dogs, and cats of either gender. In female dogs, 50% of mammary tumors are benign and 50% are malignant. However, few of the malignant mammary tumors are fatal. In contrast, over 85% of mammary tumors in cats are malignant and most of these have an aggressive biologic behavior (i.e., mammary tumors in cats tend to be locally invasive and spread elsewhere in the body)."