How can I temporarily hide in-stock variants from my store?

[WildWesternWear]

Hi all,

I have a weird situation. I have a product that has its quantity automated by a third-party app (Spocket). However, that app has not been updating stock correctly and the product is no longer in stock on AliExpress. So I am trying to hide that specific variant from my store temporarily until they fix their stock issue both on Spocket and AliExpress. How can I do that on shopify? I don't want to mess with the current stock numbers or automation I have setup or remove the variant entirely that I have setup on my store.