I've worked with Biobankers/Bioinformaticians on this type of problem before and none of them wanted us to got the Differential Privacy route. Why? The vast majority of genomic diseases are rare diseases (with 10s-1000s of carriers). Destroying information is not an option with small sample sizes. For huge GWAS studies, it could be an option. But in the general case, security is preferable over privacy when a choice needs to be made.