Nail varnish might melt the tape I think - do a trial with it on a casette you can afford to destroy.
Here's a 1953 article on tape splicing. I have used scotch tape on a Video but not on an audio casette.
http://www.aes.org/aeshc/docs/3mtape/soundtalk/soundtalkbull26.pdf
Peccavi
December 2008