In your case you use undermount kitchen sink which requires to apply adhesives at the top of the edges. It can't be avoided because the mold will grow no matter which kind of adhesive you apply, even you use cement it will still grow. But if you dont want to apply the water will leak through there. Only solution is temporary which is reapply the silicone from time to time.

Another long term solution is change the kitchen sink to countertop kitchen sink which the edges are on the top of your table. Then you apply the adhesive under the edges so you wont see it even if it grows mold.