You absolutely need a fan shroud, It's there to draw air in through the radiator & fan. Your cooling system will not work correctly without it.Dumb question but what is the purpose of a fan shroud? No major off-roading planned. Does one even need it?
FWIW I always remove the four bolts from the water pump pulley (the ones you circled in blue), but I also usually remove the belt too which generally makes it easier to access everything.
Also - be CAREFUL when you get the fan loose & pull it out of that engine bay. The fan blades are sharp-ass steel & will put a hole right though your radiator if you aren't paying attention. Ask me how I know..