It's not a stupid idea but super glue is very thin and tends to get messy.
What about going to a nail salon? They may be able to use some of their high build adhesive to seal up the area.
They use this adhesive to fill fake nails as the natural nail grows underneath.
I can't imagine them charging more than a few bucks to do the job.
( I only know this because I have two daughters 21 and 22
)