I would recommend you the Microsoft Wireless Mobile Mouse 4000. It´s not expensive, is well built and works really well. Plus, you get side-scrolling in the wheel as well as a customizable side button and a on-off switch. In the packaging it says the battery lasts up to 10 months, altough i've had not used it long enough so see if it's true, but compared to an older mouse i´ve had, which would eat out 2 full batteries in about 12-20 hours time, it's holding together pretty well!

EDIT: Just as i posted this and took the hands off the mouse, the red low battery light started blinking, so now i can tell you you will get at least one and a half month on one Duracell AA Battery. Still, pretty good life compared to what you're currently facing. And a quick update about it's side button (because only now i saw you don't want a side button at all): you can configure it to do absolutely nothing when pressed ;-)

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