I don't see having a mobile optimised version of your site will have a direct impact on SEO. However it should reduce your bounce rate you're right.
I would suggest going down the responsive route instead of another site or sub domain just for mobile. Although it's technically not a redesign and you should be able to get away with minor changes to the underlying HTML code, you need to think about your site from a mobile customers perspective. They want very different things than a traditional desktop user.
Sitepoint have a very good book on mobile website optimisation that I would recommend reading.
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