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This is how mine looks, to give you an idea of what you might expect. The kind of mottled look is, I think, a pretty normal consequence of the shredding/re-forming process.

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Because the...

Nope - no melting required using this method. Some soaps can be heated and melted but my understanding is that this is a bad idea if you have an essential oil soap as it messes with the scent.
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Welcome Jordan!

I have never used a shavette and so can't help much on that front, but I do have a suggestion for your bar of soap. Get yourself a bowl that you don't need/use for normal...