The mouse doesn't affect the smoothness of the meter in any way, shape or form.
The "stutter" can however be caused by one's computer updates "behind the scenes" (on weaker machines) or a flailing internet connection. Every time I get a choppy meter, it's followed by a "resolving shot" spin...
The stutter can be caused by other issues as well apart the ones Jures has mentioned.
1. Refresh rate. Check your refresh rate to be either at 60Hz or 59,94Hz.
2. Temps. Check your PC's temperatures while playing.
3. Low free ram.
4. Weak an old cpu.
5. If you are using some old version of Intel's ingrated graphics is not the best for smooth meter.
The batteries of the mouse (wireless) will affect the input and output lag aka the responsiveness of the click. In no way it can affect the smoothness of the meter. If it wasn't so, it would be like saying that if my wireless keyboard battery is running low, i would be having juddery videos or meter in games. Not the case.