Is it possible to manually trigger a survey being sent to a customer?
Surveys aren't tied to the notifications that go out, it's the structure of the survey link that attaches it to the item it was sent from, but only when the end user clicks on the link to start the survey session.
This allows you to build a quickaction that uses the same HTML source as your survey notification and have it function in the same way. As long as the survey link is correct in the manual notification, it will link correctly.
This also allows you to manually 'Re-Send' a survey if you find one did not go out as expected.