So they were lost during the day when they were free ranging I take it? just the hens no roos? this sounds more like theft to me
I take it you were out at the time? giving eggs to neighbours is all well and good but they just have to talk to other people and word gets around that you have chickens... in any case I would not use snares, I understand your frustration at the culprits involved but snares are horrid things and cause alot of suffering to whatever may get caught, it may be better to set a cam up as you suggested and see what you are dealing with here first and then take action appropriately.
