While it’s true that states might guarantee these rights, it is not true that doctors will behave in the fashion you suggest. The facts: Abortionists (who are usually primary-care trained) make more money than even the most talented and highly-trained specialty surgeons. Abortion is a cash business—the MDs bring in a million a year. Even with that money, finding an MD willing to do it is hard. What you suggest would cost a doctor his license, for very little financial reward. Ridiculous suggestion.
It is NOT RIDICULOUS at all. Doctors have been performing abortions as D&Cs since the early mid 20th century at least. No one would ever know, unless an actual pregnant woman who wanted to abort and still hurt the doctor set him up. When one of our recent Presidents got his girlfriend knocked up this is how it was resolved back in the 1960s.
It would take a certain kind of doctor to break laws and do it, but they are out there. Please remember that we are talking about doctors who performed abortions several times a week until their state chose to make it illegal. So this doctor would have sympathy for the patients who are in this predicament he used to solve so easily. You see?