Not all inbound shipping is a COGS - right?

I have a mental block about most accounting concepts and COGS and shipping is a big one!  OK, just for a sanity check can someone (or multiple) confirm the following:
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[*]Not all inbound shipping charges from suppliers are COGS.  For examples a shipment of office supplies would not be considered COGS while a shipment of raw materials would.  I am correct that we must post vendor shipping charges to a minimum of 2 accounts: a COGS shipping account and a normal EXPENSE shipping account.
[*]If a Bill from a supplier has 2 lines, line #1 is office supplies, line #2 is production materials.  The Bill has a single shipping charge.  We would need to break that shipping charge up and post the appropriate portion to the COGS shipping and the balance to the EXPENSE shipping?  (this is basically an extension of question #1)