When configured properly, Odoo will book a Landed Cost adjustment on a Drop Ship Transfer to cost of goods (based on the Expense account setup on the product on the Drop Ship Transfer).
Check you have a service product with the "Is Landed Cost" option checked so that you see the CREATE LANDED COSTS button on the Vendor Bill as soon as you add the service to the Bill. Be sure to click this button to process the landed cost with your desired split method and choose the drop ship transfer.
The account that is debited on the Vendor Bill line for the shipping to be landed is the Stock Input Account of the Product Category that the landed cost service product belongs to. This debit is only transitory/temporary as it will be cleared when you process the landed cost and become a debit to cost of goods. The default Stock Input Account is the Stock Interim (received) account but you are free to change this to any reconcilable interim/clearing/wash account.
Whether you add the Landed Cost to the same Vendor Bill you use to pay your Vendor for the drop shipped product, or another Bill from your shipping Vendor, the landed cost will work the same way.
Odoo will not adjust the cost of goods on the Customer Invoice, since they product is always simultaneously delivered and received on a drop ship - the cost of goods will simply be debited at the time of processing the landed cost as a separate entry.
The journal item from the Customer Invoice as well as the Journal Item from the Landed Cost adjustment will record the product - so you can see your true cost of goods per product by grouping the debits in this account by product.