Any woman who finds herself pregnant , when she hadn¨t planned to be, is justified in asking for a paternity test, as indeed is any man whose girlfriend informs him that she is pregnant.
In this day and age, it is hardly an insult to ask for this, and may indeed be a legal necessity if the mother is to be able to claim financial support for the child. The child's birth needs to be registered, and she will need to know whether to fill in your son's name as the father, or state: father unknown!
It cannot be in you son's interest to pay support for a child that is not actually his. Nor can one reasonably expect a woman to bring up a child entirely on her own unless she is very comfortably situated moneywise,
From an entirely different point of view, all children have a right to know when old enough, who their birth parents are, whether or not the father choses to be involved in the child's life in any way.
Stop shilly-shallying and demand the phone number or address of the woman concerned next time you see your son.
If he does not want you to approach her, the onus is on him to tell you why. You do not necessarily have to go along with his wishes.
A bairn is a bairn and should be made to feel welcome, and any pregnant woman placed as this child's mother is, is likely to be touched by the prospective paternal grandmother getting in touch.
Many musicians and other artists are financially insecure - most support their children either as well as they can, or take some secondary job that puts food on the table.
If your son wants in some way to be part of this child's life, he will need to find a way to do so, or else, he would be better off telling the woman concerned that he wants nothing to do with her or the child.
There are two sides to this as to any other story. The woman has unilaterally made a decision to have the baby - good for her, but she may have to accept that the child's father either cannot or will not help in any way.