Little Nell instrumentals are probably going to be near impooible or very very very hard to obtain/create.
Several years ago the folks at the Shock treatment Network (now defunct)created an instrumental for Beauty Queen BUT the only reason that was even possible is because of the stereo recording, (Little Nell's vocals were on the stereo channel right while the music channel was on the left; they simply deleted one channel and created a Mono instrumental track). You could ask someone here if they are willing to upload that version here in mp3 form.
Little Nell's other singles aside from Fever, Do the Swim, and See Ya Round Like A Record are only available on existing vinyl and thus makes it hard for anyone using any kind of computer program to delete main vocals and create a karaoke style track. Those analog recordings just weren't built for that. Her singles (the above mentioned)that are avaiable on CD form might have a slight possibility of having the vocals removed (up to a point) BUT will not be anything near an instumental or karaoke track....sorry to say
Steps to creating a beauty queen instrumental:
1. get beauty queen on rockymusic.
2. open audacity.
3. turn the pan knob (center) until it says pan 100% left
4. export file as .wav
THERE! You have your own beauty queen instrumental.