As of now, this is only possible in code. I wish Shopify would give us more control over variants natively instead of peddling third party apps to us.
In my own store, what I did was to hijack the "This is a physical product" checkbox to use it as a checkbox to show or hide the variant on our website. Since this manifests in Liquid code as "variant.requires_shipping", I wrapped the relevant code with "{% if variant.requires_shipping %} ... {% endif %}". If I disable the checkbox, that variant doesn't get shown as an option in the website at all. The checkbox was fine for me since normally all of our products require shipping, so I'd never legitimately turn the checkbox off. So it made sense for me to repurpose it. Of course, if you already use the checkbox to actually distinguish shipped vs non-shipped products, you'll have to find something else that's unused - like the Compare at Price (set to something weird like 0.01), the Barcode or the SKU fields (set to a very specific phrase, like HIDETHIS).
Unfortunately this only works in the Online Store. There's no way to control the variant in other channels yet, until Shopify gives us complete control to turn a variant on or off within the Admin site.
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