I was afraid for that too for many years. Till I used a cordless one from my son.
The cordless one is more accurate. If I put it on my charts on a position and remove my hand from the mouse, it stays on the position. If I do that with a corded mouse, most of the time the mouse still moves when I remove my hand because of the tension on the cord. Very annoying.
I bought a cordless for around $20 and it works on 2 AA batteries. It works for many weeks, even months while using it intensively for at least 12 hours a day. I always have 2 extra, loaded batteries to replace when needed. Replacing takes just seconds. So weak battery is no issue at all. And no annoying cord anymore.
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