How to send customers from a second Shopify instance to Klaviyo?

Hello, for my brand, we have an additional Shopify instance we use for ‘gifting events’. It is a duplicate of our DTC Shopify but products have no prices. Our sales reps at large events use tablets to create purchases in this ‘gifting’ Shopify instance with customers that come to our booth. 

This is not a Shopify instance that customers can access otherwise. We’re not necessarily interested in their Shopify data, perhaps besides the gift they chose. 

We would like to send these customers from this gifting Shopify instance to our Klaviyo. I am looking for an automated solution so that when a customer enters the gifting Shopify instance, they will immediately be sent to our Klaviyo. 

But our Klaviyo is already integrated with our DTC Shopify store.

I was wondering if anyone had any ideas for a solution here? 

I understand that a 1:1 Shopify to Klaviyo instance is recommended, but I am trying to explore the technical options that would allow us to send these gifting customers to our DTC Klaviyo. 

Thank you.