Parts of my rig do not export properly to Collada or FBX format

I recently modeled and rigged a character in Blender, and within the .blend file itself the character moves properly with the rig. But when I try to export it in a common format, the rig breaks. Meshes that were parented to a bone with no deformation are no longer parented to that bone, and sometimes they’re gigantic compared to the rest of the model. And that’s even after I applied all scale, position, rotations to them.

The rest of the meshes, the ones that have weight painting and bend with the bones, properly export. It’s just the objects that I want to move with a bone but not bend.

Edit: If you need to see my blend file to see what I mean, here it is:

I use Blender 2.79 because the interface is more familiar to me. I’d prefer if the solution is something I can do in that version.

have you got any rig that drives the skinned skeleton. If it’s the case select your skinned bones and bake the animation on selection. then you ll just need to export this bones and your meshes and perhaps a root bone with no skinning .
but perhaps, i’m wrong

I’m not sure what you mean. Do you mean animation data? In that case no, all i have is a skeleton that this model is rigged up to. I just want to export this model as a .dae or .fbx and retain the entire rig, including the hands and head, which currently lose their attachment to the rig when I export it in those formats.

Ok, i’m gonna check the file.

What i finally observe after many exports iteration, is that only the objects with skinning datas are sticked to the bone.
The rule mainly when u export in real time engine is, to skin everything and really often in one joined object.(to avoid a lot of object matrix to manage)
but i guess, due to the objects in your scene, that you plan to swap meshes with code.
skin everything on the skeleton, instead of parenting them to bones.

not an obligation:
Join meshes that dont need to be swaped in game together ( after the skinning process it ll be faster for managing weight groups) and leave the others as objects.