What's the best way to make a barb fitting that's a bit small for the tubing give a water-tight fit? [See details].

For what a reducing barb coupling looks like, see this. It’s the actual part in question. I knew I really needed a 5/16” x 3/8” barb fitting to give a snug fit on both hoses. But I found nothing even remotely like that locally and had to run a long series of searches to finally find the one linked above. In fact, USspaParts.com is who I got it from.

I figured that at worst case, I could use a small hose clamp to make it work. But is there a less unsightly solution? Could I use a caulking gun and some form of plastic to build up the ridges? Any ideas for a fit fix that won’t leak, still leaves the hose removable, but doesn’t stand out lie a sore thumb?