If you don’t want to store it in a column, my suggestion is an action like this in the inline list that shows the “item”:
1/Show details view
2/Webhook/Zapier action that has the “link to current screen” as a value to pass to Integromat/Zapier.
I assume you’re writing the shortened deep link back to Glide, if you’re using Short.io, so your custom action branch that includes the Webhook/Zapier action only needs to run when the shortened link column is not empty, else just show details view.