I'm going to use my baby's father's credit card to buy a stroller without telling him.
Why do you feel like you need to do it in secret?
He refuses to be part of his child's life.
Wanting the father to take some responsibility is only natural so I can understand you feeling frustrated with him but that doesn't give you an excuse to steal from him. It's not okay to steal from anyone, under any circumstances. You should ask him to help and if he refuses take him to court.
I don't want to go through all that trouble, I just want to make him feel some of the financial responsibility.
If you have not made a formal claim for child support from the father, then what you are doing is the same as theft.  Even if you don't want to go through the trouble, the father could end up taking you to court, and that would be much more hassle for you.  I think that you should pursue compensation legally.