I remember at one of our rendezvous many years ago Jim Skoggins was giving a demo on coyote trapping. He mentioned catching the occasional non-target cougar. Someone asked Jim, "how do you tranquilize them?" Jim's reply; "with a 30-06". Of course we all had a good laugh.
I think that might have been the option I would have chosen in this "bear in a wolf trap" situation.
Oh I remember that story like it was yesterday.

Eric Digman released two black bears out of his wolf traps last season over in Idaho. One adult and one cub with momma bear not to far from the cub.
He had his Grandson with him on one of them and had his Grandson hold on to the rope while Eric released it.
When you see Eric, ask him to tell you that story.
I mean Wow.
JC