A tap would be for repairing or cutting new threads in the backing plate. Not really going to help here. Either use a drill to remove the screw head or the cut-off wheel. The problem with the wheel is that it will ruin the spinner if it isn't already damaged.

Then go out and buy some decent screwdrivers. Stripped/damaged screws are often caused by cheap tools. Don't try to "make do" with something that that just about fits. The right tool for every job makes life a lot easier. More expensive but easier. How many destroyed parts before you have paid for that new screwdriver?

Here's a tip: don't buy your tools at Krogers.