Keep in mind that the CSS profile is a repository for documents. Like the FAFSA the profile simply collects information that can be sent to multiple schools.
Just because a school does not use the non-custodial profile does not mean that it will not need or ask for the financial information of the non-custodial parent as many schools have their own financial aid forms.
Your best bet is to go to the financial aid website and carefully read the instructions to apply for financial aid. In addition, every school has a net price calculator (this may not necessarily be the most accurate when it comes to. divorced families, business owners, and people who own real estate outside of their primary home).
You must make sure that you are using a bottoms-up approach in making sure that your child(ren) is looking at schools that are financially feasible options for your family. You must have a 4-year plan for financing college. a dream school should not be a financial nightmare. If your student is borrowing more than $27,000 you may have to reconsider.
If the journey has to start at a community college for affordability, there are schools that have great articulation agreements with 4-year colleges.