The gentlest we have seen is a sedative (It can also be injected in the
thick of the thigh.) and then when the ferret has passed out after
getting groggy in our arms with lots of kisses a heart stick while
unconscious. Like you we have seen several methods. Sometimes if the
ferret is actively dying but in pain so needing help then the sedative
is enough to take them.
[Posted in FML issue 4877]