Hi, @ChristopherRice - We've had similar scenarios at our institution. This can be accomplished by creating an assignment (with text entry, for example) and putting it in its own module. You can then set the requirement for that module to be a nominal score (say, 1 point). Once the student has completed all of the course requirements, the instructor can go to the gradebook and score this assignment as 1 point, which will then trigger the completion of the module, and hence, the course. So this is something of a dummy assignment, which gives control of triggering completion to the instructor.
You can include text in this assignment that completion certficates will be sent once the instructor has reviewed the required work for the course. (Note that the student would not have to submit anything for this dummy "trigger" assignment, but you could use this assignment to collect feedback on the course, if you wish.)
This is one way we've managed this kind of need -- hope it helps! 🙂