I came across this post looking for a way to get 8khz consistently (I use a Viper 8k as well), and I still havent, but I figured I would share my findings as they may help you.
1000 and 2000 hz work reasonably well (as you already know). There is a performance hit on 2000 hz over 1000 hz, but I find it to be negligible, especially on a modern gaming pc. I recorded an FPS difference of around 30, which isn't that big a deal in a game like osu where you can easily reach 900 fps on a 15-year-old graphics card.
4000 and 8000 seem to work relative to system resources and osu updates.
Since a higher polling rate puts more pressure on your CPU, I would first suggest limiting background tasks.
With CPU and RAM at a low utilization, I can get 4k to work smoothly. 8k "works" but with occasional hiccups. Unfortunately, these hiccups are bad enough that I still wouldn't suggest using 8k, especially if you are trying to improve, as it will certainly cause unintended misses and lowered accuracy.
As far as 8k goes, there clearly seems to be something going on on osu's side. I've had the Viper 8k since it came out and I've seen wildly different performance between updates (I play on cutting edge, not stable). Some updates it works perfectly, as if it was made for it, others get the awful stuttering you mention (where the games starts lagging the second you move the mouse cross screen). One time it refused to even work at all (worked on the desktop and in other games, but tabbing into osu caused all functionality to cease). For now, we can't do much other than wait, as the technology is so new that even few AAA games are adding proper support, especially with the niche market it's currently in.
I personally find turning V-sync on also helps, but I am unable to tell whether that's placebo or genuine performance; maybe it just makes the stuttering less noticeable, but it did "feel" smoother.
Hopefully you can get some added performance from that information.
Lastly, please kindly ignore the few who feel the need to go on a misinformed crusade over using 8k hz. 1000hz polls at around 1ms, 8000 at around 0.125. This difference is not negligible and beyond noticeable. While you still need the skill to back it up, and it will take some time getting used to, anyone implying that 8k hz doesn't make a difference is likely just employing a "fox and the grapes response". Remember, they did the same thing with high refresh rate monitors, now those are a "must have". Where will 8k mice be in a year from now?