Blender - Rigify, Child Of constraint FBX export issue

Hi guys. I have this isssue with rigify inside UE4.

I have Gun bone attached to Hand bone via Child OF constraint. In Blender it follows hand perfectly, but after exporting FBX file and reimporting (no matter if it is inside Blender again, UE4, Unity), Gun bone slighlty moves against Hand bone (see attachment rigifyIMPORT_fbx.gif).

The weird thing is that when I have created basic IK rig and attached Gun bone to the Hand again using Child Of constraint - it runs perfectly after importing FBX ( see basic_rig_imported_FBX.gif).

So my question is that this is Rigify issue ? I tried to bake animation, attached bone to Empty and doesnt help. I know Child Of constaint uses World Space. But it works good in basic rig with simple IK. It will be great to find a solution. Thank you.