Hello, @ajhall24!
Go into your gradebook for your course. You can do this for just one assignment by clicking on the three dot menu for that specific assignment/quiz and choosing "Hide grades". You'd want to do that right away before you start grading, or if it's not available before you start, right after grading the first exam. Then, when they're all graded, return to that same menu and choose post grades.
Or, you can make this your default by going into the settings wheel in the gradebook, going to the grade posting policy tab, and choosing "Manually post grades". All assignments and quizzes will remain with the grades hidden by default until you go to the three dot menu and choose post grades for each assignment. I personally use this option so I can double check for any errors or do that hand grading you're talking about before anyone sees any grades. Saves me many a student freak out. 🙂