We have ALOT of havaheart traps. Probably 16-18 single door coon size 2-3 XL double door coon atleast a dozen of the single door squirrel size 1084 Im 99% sure.
Along with huge custom made traps for dog/coyote/turkey sized animals.
I think you are going to have a heck of a time trying to live trap a weasel of a mink. They are very wary , mostly hunt live prey ect.
I think a hole set conibear or leghold possibly even a log set leghold will be your anwser. That or .22lr with a scope. They are very wary animals.
If you DO decide to live trap I would build a trap box out of some plywood to put over the trap to make it look like a hole. Id also avoid as much human scent as possible and place it along a fance line or against the side of a building on a known route. Make sure the trap us VERY stable with no rocking!!!! If you are successful you will need to dispatch them as moving predator is a bad idea. They mostly try to return home crossing other animals terretory fighting and risk speading diease.