There is a list of CSS Profile schools at https://profile.collegeboard.org/profile/ppi/participatingInstitutions.aspx (the list has a column indicating whether NCP information is needed).
However, while the set of FAFSA-only schools is a very large subset of the complement of the set of CSS Profile schools, it is not the same, since some schools that do not use CSS Profile have their own supplemental forms (some of which require NCP information). In addition, the CSS Profile list linked above may be out of date or have some incorrect information.
Check on the college’s web site to be sure of what financial aid forms it needs.