Boiler makes a good point. It doesn't really matter what degree you have for the most part. Some careers is does matter. I put down criminal justice or finance because that is what I am interested in, and yes a degree in criminal justice does help you in other law enforcement related jobs, not just a doughnut eating cop gig.
I say get a degree in something else so at least you have some knowledge in some other area you may enjoy so when you fail your medical you can have an easier start in a different career.