Over my years of backpacking, I carried everything from a 6" 44 magnum down to an NA 22mag mini.
The one time I thought I might need my handgun was with the mini revolver. It was actually in my hand in my parka pocket with the hammer cocked, before the situation de-escalated.
After that, I started carrying a lightweight Charter Arms 38spl snub, which I felt gave me a more effective weapon at little weight penalty.
As for the LCP, I have a similar p3at. It's a good pocket gun, but a light 38 snub is still easier to shoot at a distance, and I believe being able to reach out is useful for a backpacking gun.