To me, it seems you have a problem of convenience here, wireless mouse vs. short battery life. If your previous wireless mouse died in the middle of the battle, then to me it's a no brainier: get the wired. If not, go for the wireless, every cable you don't have cluttering up the back of the desk is gold :-)
For the rest, I'm with p3lbox, mouse technology has advanced to the point that more or less all mouses are indistinguishable in usage. Although I'm not suggesting that a $3 mouse will do the same service as a $30 one (I know for personal experience that this is not the case), spending $150 in one just for a supposed increase in the response time is wasting money. Of course, such mouse will get you other goodies that justify the price.
Perhaps a professional gamer will be able to appreciate such differences due to their endless practice, but anyone else will headshots aplenty. Most times we blame the peripheral, while the problem is with a miscalculation in our part.
Besides, people are playing CoD 4 with a XBOX pad