Will a New York judge grant an uncontested divorce for adultery?

My wife cheated on me and I want a divorce. We have not been married long and have no kids, and we have agreed on how to split up our property. I’ve been told we can get a quick, uncontested divorce as long as we both agree on everything. I agree on all issues except why we are divorcing. She wants to say its ‘irreconcilable differences’ and I want the divorce decree to say it was her adultery. I’m catholic and I want to get the marriage annulled in the church once the divorce is over, and I need to show she cheated on me to do that. Can I get an uncontested divorce if I want to pursue it based on adultery?