If you really want to switch SkeletonDataAssets, this can be done like this:
public SkeletonDataAsset otherSkeletonDataAsset;
void SwitchSkeletonDataAsset() {
SkeletonGraphic skeletonGraphic = this.GetComponent<SkeletonGraphic >();
skeletonGraphic.skeletonDataAsset = otherSkeletonDataAsset;
skeletonGraphic.initialSkinName = "YourNewSkinName";
skeletonGraphic.Initialize(true);
}
However I would recommend enabling/disabling GameObjects, as you then only initialize once at startup.
Another simpler solution: Have you tried increasing atlas images size so that both characters fit into a single atlas page?