Keep playing animation smoothly when switching models

Two models have same bones and animations, so one of animations can be played even though model is switched. During switching, the second model is loaded asynchronously and the animation status is saved. The first old model is disposed and removed from the scene, then the second model is added to the scene and animation is played from the saved status.
However, when the model is switched on screen, just break or short pause of animation can be seen and very small period of animation is skipped.
Welcome if someone has already experienced and share the solution about how to fix. It would be great as well for any advice.