Safely remove external hard drive before i shutdown?

the shutdown process will disconnect all drives and devices safely. Sleep may or may not (depending on your version of Windows).

Keep in mind that if you are on a Windows PC there is a fair amount of fault tolerance and so long as you are not actively writing to the device while removing it then there is little to no risk of corrupting anything. Mac OSX will complain a lot if you do things improperly, but (for the most part) it shares many of Window's protections against corruption.