In Wisconsin, can a father sign up parental rights without the mother agreeing?

A father has parental rights, just because he is the father, if he is not listed on the birth certficate and the mother is not agreeing.
The father can file a request in court for a DNA test, and for partial or joint custody, for visit rights and every right he can have.

And of course often the mother does not agree, but every father has full rights as a father, after the DNA test, he has all rights as any father

You should be able to acknowledge paternity formally by completing a form (look up the laws of your state) and filing it and/or register as the putative father if it's before birth or within a month or so after. Then when you go to court they will see you did everything you could to accept responsibility. They may still order a DNA test.