Hmm, I always exfoliate the day after shaving, like Purplepixie said, it stings to do it straight after. I don't use anything perfumed and use non-soap too and I have tried all different types of razors, product (while shaving). So maybe it is just me and my skin.
It was only the other week that a friend told me you should exfoliate before shaving but that has not helped either.

I have a glove, would trying to exfoliate on dry skin be better or should it always be wet?