So obviously you should be allowed to use Item Upgrades in the All Cups NG+ category. But what about Single Cup Runs? Am I allowed to buy, for example, the shield upgrade and use it in a Krazy Cup Run?

I am not a mod, but in the past, I have used a shield upgrade in some of my single cup runs and they have been accepted. The single cup, the only goal is to get the fastest time. So upgrading your shield just ups the chance you are going to get one in a run. Even then, it's not like you will get one every run. So I would say go for the upgrade, and may I see some of your times on the leader board. Godspeed!