Mice can be of varying quality. Your hard-wired mouse can be of higher quality than your wireless mouse, which is why it may be performing better. (And not because it's hard-wired.)
I've played this game with a great variety of mice (they always seem to break in this household), including playing this game on a TV set while lying in bed with a wireless mouse on my belly. Never had any problem. I've recently purchased an expensive Gigabyte wireless laser mouse, and its precision compared to every other mouse I'd tried before is incomparable. Basically, you get what you pay for.
There should, however, be no problem playing this game with any wireless mouse. (More issues are reported when playing through a wireless network, and I'd caution against that.)