Many lenders still do stated / stated loans, especially with large down payments. And usually 25 - 40% is considered large - depending on the lender. You might want to look into conserving some of that down payment for a possible "rainy day" or to purchase an investment / vacation home down the road.
I would be happy to refer you to a good lender and / or discuss your situation with you more fully. I might even be able to give you some insite on how to move forward after your divorce (I went through the same experience approx 10 years ago, with the added complication of a foreclosure, and now own multiple properties in multiple states. It is doable with the right planning and the right professionals to help you get there). You can contact me through my profile.
I am confident you will find the right home, at the right price, with the right financing and Dare to Dream.
Real Estate Consultant
RE/MAX Palos Verdes Realty
Take your time, invest wisely. You are trying to build wealth.