Typically the wireless mice connect over noon-bluetooth wireless protocols and offer bluetooth as fallback, if at all.

Click-to-screen latency is a combination of reporting rate, polling rate and latency within the software stack. Default USB HID polling rate is 125Hz so if you don't do anything extra on top this is what you get anyway. Even higher grade "office" mice offer higher reporting rates than that, "gaming" mice can easily be 1 kHz.