Is it possible to trigger an event off printing a picking ticket? Or failing that, disable editing sales orders for specific roles if the picking ticket has been printed?

Second one should be pretty easy, there should be a checkbox on sales orders for ticket has been printed (cant remember exact name). Just put a workflow on sales orders that triggers when that box is checked and remove the Edit button.

For the first question - there is a User Event context for print you can try use.

context.UserEventType.PRINT