Oh well, you are screwed
Regardless which 3D editor you are working with (assuming it is Blender), there is GOLDEN rule when you have to export to FBX and specifically when attaching mesh to armature.
Before attaching to armature, you must reset Scale, Location and Rotation of the object as well detach it from any Pivot nodes (Empties in Blender).
It has to be just a mesh with Origin/Pivot Point preferably located at 0,0,0. But the Scale reset is the most important.
In Blender it is CTRL+A in Object mode. Otherwise, it might work in some cases, but in most of the other cases you'd have a lot of problems with prop which was not originally reset.
As you said, you cannot take that prop to OBJ because of the bones, so you'd have to take it back to 3D editor as FBX, detach from the armature, properly reset, re-attach, weighted and export again.
Once in iClone you can change the Pivot as you wish and it would be just fine.
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