HI RA31596, a good thing would be to have the parts that need to smootly transition from one position to the other be separate, for example have the nose separate from the base of the face, so you can move the nose from one position to another in a smooth way.
Another thing you could do if you can use meshes and maybe you have two different flat drawings is maybe trying to get them both at a middle point where they're both very similar to each other so that even if you change one attachment with the other, it won't be as snappy.
You can have snappy changes from an image to the other, but stretching out secondary motion at the extremes should also help making the transition feel smoother.
An easy example of what I mean with using separate pieces is to be found here: Twitch: Mermay? Mermeow! - rigging a simple character turnaround in Spine Pt.2 - YouTube and at 2:46:30 the kitty is turning. Now, this is a very easy rig to demonstrate a technique, so depending on your drawings, you'll probably need more work.
Here's a GDC talk explaining how to smooth snappy animations: Making Fluid and Powerful Animations For Skullgirls - YouTube