You can just modify your sim into a nano sim. There are already Sim cutters around that will cut a regular/micro sim into a nano sim.
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You'll have to wait until they are more widely available as they're just rolling out.
The thickness difference between the nano sim and micro sim is 0.09 mm, less than a tenth of a milimiter. All electrical connectors have some tolerances to them, otherwise they wouldn't work. And the toleranceswouldn't show any difference to a tenth of a milimiter. A tenth of a milimiter is less than the thickness of a really thin sheet of paper.
Unless the iPhone uses some sort of ultra thin ultra precise sim reader, you shouldn't have to sand the bottom in addition to cutting it, but if you do it will take only a few passes with 2000 grit.
Hope that helps.