Hello David, 

Below possible ways we can implement inventory for this with common assumptions that the DropShipper (users ) who are currently holding inventory and delivering on the request are ready to update Inventory Records on Odoo.
Approach 1 : Create Separate warehouse as Drop Ship warehouse and provide the limited access deliver only for that separate Warehouse. And in such dropship products you can manage/configure the routes to get that delivery created from that DropShip Warehouse based on the product included in the sales order. (this might need little customization)

Approach 2 : Create Separate Company within your Odoo as DropShip Company and provide the access to the dropship warehouse users. And Create the automatiion to create the deliveries only for the Selected Product to that Drop ship company.

On separate notes, If the dropship company is totally using different software system of their own, then we need to determine the Data interfaces (pushing the Delivery Data and Pulling the Stock Levels in realtime). In this case it will be the Integration developing approach.

Thanks