No alternative?
Well, not for do-gooders, anyways.
Dart the critter, then while he is conscious but immobile, bet the crap out of him. (A broken rib or two - the gift that keeps on giving - is a plus.)
Then, chuck him in the back of a pickup, haul him out in the woods and dump him. (Well, in this case, I guess it’s got to be the WPA created Nebraska National “Forest”.)
Before leaving Mr. Kitty, apply a second beating, then liberally apply a coat of human urine and feces. That way, humans smells become associated with “From now on, I’m gonna give those two legged animals a wide berth.”
Of course, do-gooders would never think of doing that to any of Mother Nature’s creatures. They’d rather kill the beast, then blame us for encroaching on their territory.
A mountain lion would be highly unlikely to survive the treatment that you suggest. Why bother?