I'd recommend using your item numbers as the SKU for any individual product that doesn't list options, adding single variants to products which don't need them would be time consuming and cause a lot of unnecessary problems. Every product has an item number already, so best to use that.
If you are using our system to send information to your fulfillment house, this page explains how we post order and item information:
For example, "item_numberX" is the variable for each item number on an order, with X being its position in the cart. "Item_number1" would be for the first item on the order, and so on. The option values selected for any product are also always sent in a similar way.
As for the actual SKU entered in the Variants screen, that will only be sent if you are posting that data straight from a particular product, and it will be sent in a variable named "sku." You probably won't be sending the data to them in a way that includes this variable, since it would mean posting the entire set of order data over for each product ordered.
If your fulfillment house is not willing to work with the data as we provide it you can probably solve the issue by having a script created to handle the data from us and assign each unique item and option combination to a single specific code which will be passed on to them as the SKU. That's something a developer could prepare for you if you aren't sure how to write such a script yourself, you can find experienced developers listed here: