do safety engineering schools exist?

Look at “3-2” programs with a careful caveat emptor eye. Financial aid that may be awarded by the “3” school will not usually be transferred to the “2” school, and many “2” schools will not offer financial aid to the student in this type of program. You will need to spend an additional year in school and thus will not be in the job market until a year later, which is a significant opportunity cost. The additional degree in liberal arts you get from the “3” school (if that is what the 3-2 program is designed for) is not of much value to most engineering employers, it is the “2” engineering degree that will be the basis on which they will evaluate you as a future hire. I usually recommend against 3-2 programs for this reason. If you want to be an engineer, you are better served starting in an engineering school and finishing in 4 years (unless you are on a co-op program which also takes 5 years, but that program will give you experience in industry and a salary which IMO is more valuable than the additional degree with respect to your career after you graduate). Don’t discount minors in engineering schools as others have stated.