I deleted the update file for iOS 9.3. Is it possible to reinstall it?
Apple has pulled the iOS 9.3 update for some (older) devices because of a bug that could prevent using your device. Apple is not signing iOS 9.3 for your iPhone (5s and older), so it is not possible to update by official means at this time. According to the link below, 9.3 could potentially brick an older phone under certain conditions. 

Source: http://9to5mac.com/2016/03/24/bricked-iphone-5s-5-ipad-2-ios-9-3-fix/