In general the Rabbonim are loath to designate anyone a Mamzer
There was a divorce case in Israel where the man did not want to pay child support for his wifes 2 kids and claimed the kids were not his. They did a DNA test and it showed he was the father of one but NOT the other.
The Beit Din still made him pay child support and refused to terminate his parental responsibilities to this child who really was a mamzer (The reasoning was a child born to a married couple is the husbands child)