Hi Fred,
No need to create 2 external web service integration's separately for tenant wise. After moving patch solution to the production tenant we just need to replace "WSDL file location" by downloading the production tenant WSDL in wsid file.
And after replacing we just need to save it, we don't have an option to activate individual file in production tenant.
So, it will work perfectly in production tenant as well.
Regards,
Shiva G