I think that there is no simpler solution than DaMage's one, with my additional changes:
1. Import your armor.
2. Import another, vanilla armor with parts you need. In this case, if I understand correctly, arms.
3. Delete everything from vanilla armor you imported except the arms.
4. Select your "shoulder armor" (make sure that in edit mode all vertices [those points between lines] are selected also), then shift select the vanilla armor's arms.
5. Go Object->Scripts->Bone Weight Copy.
6. Set quality to 3 or 4, and select 'Update Selected'. Hit Okay and let it work, this can take some time depending on your computer's power.
7. Delete the vanilla arms.
8. Go back to object mode and with everything unselected, import the skeleton.nif found under meshes\character\_male\. Remember to select 'Import skeleton Only + Parent to selected'.
9. Select all the armor pieces and then lastly selected the skeleton you just imported. Hit ctrl-P key and select the first option each time. Lastly hit ctrl-A with everything selected.
10. Export, you've rigged them all to the same skeleton.
Try it a few times to understand how it goes. If points 4-7 doesn't work with arms, try pauldrons. You can recognise that the rigging has been added at all by opening exported mesh in NifScope and checking does this particular NiTriStrips/Shape has NiSkinInstance part.