I just did a test, recorded my bass guitar through a high gain distortion pedal and then direct to my sound card at 96kHz/24bit, and then using a spectrum analyser, I looked at the frequency content, and saw it for certain notes extending the whole range (upto 48kHz). Now these high frequency overtones were at quite low volume, but still noticeable visibly (of course I can't hear them directly).
How high do these overtones extend, would 192kHz be enough to capture all of them or not (my sound card does not go that high)? I also assume that for electric guitars it does go a bit higher still, but just to get some idea either is fine.
And yes I did DI and not use speakers and microphones which would have put in a much higher noise floor, so please do the same. Since I'm talking about tones that we can't hear directly (possibly their interaction in chords might be noticeable if they were at a high enough volume), the requirement for the highest overtone is basically whether it's measurable in the sense of being above the noise floor.
Edit (see comment below): When looking at the overtones generated by distortion, how high do the overtones extend measurably different from the noise floor?