We have a Canadian website and a US website. All products are shared. But we have two warehouses, one in each country. Therefore we need different stock levels for our websites.
I have the exact situation as you.
In Magento SKUS are globally unique... and can only have 1 inventory level.
First off... DO NOT use an extension (AITOC multi-inventory) for this. Just don't. The answer we came to after much debate and asking around was to simply NOT use the same product. We clone the products but with a suffix on the SKU and URL slug. Now we have separate inventories... Yes we have to maintain 2 skus... but that was acceptable to us.
In our US store we have a Product with SKU AB12345-XYZ The Same Product in Canada store is SKU AB12345-XYZ-CA
Then we remove the -CA from any canada sku when we integrate to our ERP or warehouse.
Likewise URL slugs are globally unique so we also append -ca to the URL slug.
The other reason you want to do this is that you want the sku to have a base price in the native currency of each store (in our case US and Canada prices are NOT an exact exchanged rate... but have their own set market prices)
I would not go with a solution where each location uses different SKUs for many reasons:
This sounds like a non-scalable workaround.
You can find numerous extensions that support this, many are featured in Magento Connect. Try to search for "Inventory Management for Multiple Locations" and you will find a range of choices.