While in survival mode, is there a way to shoot while protecting myself using the riot shield? Or should the player switch between the weapon and the shield every time?
You cannot shoot while your riot shield is equipped. Your offensive options with the shield are limited to the Melee Shield Bash, and your Equipment. This makes the shield rather unfavorable for Survival and more of a 'toy for fun' type of equipment.
If you insist upon using it, the best way to do so would be to find a narrow hallway and have the shield on your back (where it will still offer its protection) and use your secondary weapon to fire upon enemies.
Another idea is to play with a friend, and use a buddy system, with the shield bearer acting defensively to stay alive with the primary purpose of repeatedly reviving his shield-less partner.