New skin or super glue?

My girlfriend cut her hand between her ring and pinky finger right in the webbing. It's very deep but then again it's in a place where it seems to have quite a bit of open space in the hand, if that makes sense. So she's tried new skin and it doesn't really close the wound. Would super glue be a good idea to close it up to keep it from getting infected, it has been advised that stitches wouldn't be a great idea due to the fact that it's her dominant hand and in such an inconvenient place. Please a little help here, thanks! 

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