This might not be exactly what you're looking for, but Neon White is one of my favorite games of the last few years, and it's on the Switch. I played on PC, but I haven't seen any complaints about the Switch version.
I don't really know if I'd call if a first person shooter. It's more like a first person platformer and you have to shoot some targets before completing the level. Levels are very, very short, and you'll replay them many times to shave a fraction of a second off of your time.