It's easy to connect Zendesk to SightMill - which automates the process of sending email surveys. There's no coding and it uses the webhooks API that will take you just a few minutes to start sending email surveys in response to a trigger in Zendesk (a typical setup is to send an email feedback survey from SightMill when you close a support ticket in Zendesk).
If you're stuck, please feel free to get in touch with us to help you setup the integration.