While you can get a 9/16 -> Scuba QD (I use one on my helmet for EGS) and while the amount of gas supplied in the LP hose would serve you as you expect. Your configuration would only confuse your students by how odd it would look to them. Keep a wrench in your box, and swap the hose at the first stage. It's a 30 second switch out.
BTW - Here's an example of a QD for 2nd stage (similar to what I have installed on my helmet - which is the same as the inlet on a scuba 2nd stage) ->
BTW - Here's an example of a QD for 2nd stage (similar to what I have installed on my helmet - which is the same as the inlet on a scuba 2nd stage) ->