Don't limit yourself.
A degree is not an absolute measure of competency.
What you should be asking is ‘do I have the necessary skill set to be employable?’
Basically, you should have the following skills to be considered a Competent Safety Professional:
With these, you can polish your resume and start hunting.
But, if your primary interest is not in safety as a profession, it is not worth it. Safety is a practice that thrives on passion of the practitioner.
In that case, I suggest you find your passion, then sharpen your skills in that field. It would be easier for you to get a job in an area you are passionate about, be it design, sculpture, construction, computers, etc.
A degree is great, it gives you an advantage to get into any industry at mid-management level, putting you on a faster track to career progression within a shorter time than when you start from the shop floor.
Hope this helps.