Thanks for your replies, I'll give it a try !
OK I did as you said, and textures are packed within subdirectories.
But when I try to import the skeleton in Unity, I end up with an error saying :
"Error reading skeleton JSON file for SkeletonData asset: skeleton_SkeletonData
Region not found in atlas: [name_of_the_region]"
I had no problem with the previous Export method... Any idea where this could come from ?