Hi Lads !
FYI, the solution of playing each animation one after the other gave satisfying results 
A tricky part though was to take into account joints animated in one animation, but not in others, hence keeping keyframed values where unnecessary.
The naive but effective solution to this problem was to force joints to their rest position in the animations in which they are not keyframed.
Another "trick" was to offset the animation tracks by a small margin. If an animation ends at 5000ms for instance, we make the other one start at 5001ms. This allows for the "forced" keyframes to interpolate correctly and not mess up the whole animation (strange things started happening when setting multiple keyframes at the exact same time frame, probably an undefined behavior...).
For the "reference wolf", here is what the result looks like with an exaggerated margin between the animations is set to 1s (in practice, turning this value to something very small makes the transition immediate):
Anyway, thanks @kbar and @m_adam for your suggestions, this case is solved !
Cheers,
Loïc.
).