Since 1.27v we have brand new module for collecting users feedback. This module features the following use case

• Collecting users feedback based on suggested voting options
• Collecting feedback where user enters his own feedback text

Configuration options

• ​Different URL can have different feedback options
• Option to expand box automatically
• If feedback item does not have a voting options to user is shown plain feedback form. If it has atleast one feedback item to user is shown voting form.

This module is not related to live support plugin itself so can be used separate module. So site can have questionary module embeded code but do not have live support embeded code and reverse ofcourse.

If you are not sure will it satisfy your needs I suggest just to play around with our demo and see how it works in reality.