In general, you should use the colleges’ own net price calculators over any generic ones, since different colleges may have different levels of financial aid for the same financial situation. Some colleges do point to customized versions of the College Board net price calculator, which allows you to save your information so that if you find another college that also uses a customized College Board net price calculator, you can reuse the information. But the customized version for each college should be preferred over whatever generic College Board calculator you may have used.
Note that some (like Princeton) have their own net price calculators, rather than using the College Board net price calculator. Some others use templates from other sources.
However, if your NCP and new spouse are unwilling to provide financial information, then colleges which require their information will be financially inaccessible unless you earn a large enough merit scholarship. That would make such a college an automatic reach if such a merit scholarship is competitive, even if admission would be match or safety, since admission without the scholarship would be effectively like rejection.