To build on @givemeawhisky comment.
wix-stores can track or not track inventory. It sounds like you would disable inventory tracking and manage this by yourself in a custom data collection. Then you can adjust what you display on your site using dynamic pages linked to the Stores/Products data collection.
Just to add to the idea of external access using the http-functions API. Be aware that this is not a secure API so you have to add your own security. I would take a look at the OAuth model and implement a variant of it.
With the ability to use npm modules in Wix you can enable the uuid module to give you universally unique ids for this purpose.
Good luck
Cheers