Red Lined Wrasse (Halichoeres biocellatus).....
 

A Red Lined Wrasse (Halichoeres biocellatus) is exactly what you're looking for. It's fairly unique and much more attractive (in my opinion) than a 6 line wrasse.

I've had a 6 line wrasse for for years without incident and it literally "turned evil" one day - like a light switch. Don't get me wrong; it was great at keeping pests in check and it was fun to watch it burrow in the sand (like clockwork) everyday to sleep. However; it turned from peaceful to aggressive overnight.

Red Lined Wrasses are very peaceful and to date; I've never had any issues with tank mates. It's a great hunter of pests.

P.S. - Try and find a smaller juvenile. A larger specimen may take a swipe at your peppermint shrimp. Any larger wrasse might. If the juvenile "grows up" with your peppermint shrimp; they should be safe.

I thought I read these will eat your shrimp...

I'm just going to put it out there that I've had a few sixlines over the course of my reefkeeping career and I've never encountered a d-bag variety personally. I have however seen them in other's tanks. I personally keep sixlines on my to have fish list because they've always been such good little workers for me. Granted as previously advised, YMMV, but I thought you probably might want to know that it is possible.

I have'nt any shrimp. When I dosed fluke tabs to kill clove polyps they also died.