Mmmm, interesting question. Fitting a tyre too wide for the rim will in effect change the curve of the tread, so you'll end up with not being able to use all the tread. If it was me I'd get the stickiest tyre in the size that fits the rim, or at most go up one size. The 160 needs a 4.5 wide rim, so by the time you jam it onto a 3 rim, you might be able to use only about half the tread width. Hop onto any tyre manufacturers site and you'll find something to suit.
Some folks are only alive 'cause it's illegal to shoot them....
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