You don't actually need that key. If you go left where you started to KT, you can hop right into the racing area. Then you can just run back to the paper and race him. Probably faster because w/o bomb I think you would have to KT back up out of that key room. Also, there is a vine lily at the top of that room that could be useful combined with the lightning platforms. It may only take 1 or 2 KTs.
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