Hiding inventory count at checkout

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We're currently working on a store for one of our clients with a specific question regarding insight in inventory.
See attached screenshot. After ordering more than available products, Shopify will reduce the order amount to the available stock. However, our client does not want wholesale customers to have insight in the available stock - as shown below. 

There is an option to continue selling products that are no longer in stock to prevent this from happening, but many of the listed products are produced in limited runs - sold out without being restocked. We've tried inserting the "silent" method shown here: https://help.shopify.com/en/themes/customization/cart/prevent-orders-for-out-of-stock-items without much luck. 

Are there any options to skip this step for end users? 
We'd love to hear your suggestions.
Schermafbeelding 2020-01-09 om 14.18.19.png