I found solution for same, might be helpful to someone we can use only chat without Feedback Tab using following URL
https://{domain}.zendesk.com/chat?user[name]=test%20e&user[email]=test@test.com
You can also add other fields like follows
https://{domain}.zendesk.com/chat?utf8=✓&authenticity_token=secret_token=&dropboxID=007&dropboxLocale=1&user[name]=Test&user[email]=r@r.com&chat[subject]=test sub