Like Mike, I am also surprised how well a walleye does on a stringer.
This summer, one was hooked bad, I didn't want to drag it around all day, but thought it should be kept, bonked it twice, and put it on the stringer. Hours later, it's alive and swimming fine with 2 scars on it's head. It became known as the zombie pickerel.
I portaged with a walleye on the stringer and out of the water for 1/2 an hour. It too came back to life and looked fine.
I poke through the membrane under the jaw, and not in the gills.
In the Yukon stringers are illegal. If a fish is caught, you decide then and there if it will be kept.