Commercial superglue is different from medical glue.
Although not labeled as such, over-the-counter Super Glue products contain methyl alcohol, because it is inexpensive to produce. Cyanoacrylates cure by a chemical reaction called polymerization, which produces heat. Methyl alcohol has a pronounced heating action when it contacts tissue and may even produce burns if the glue contacts a large enough area of tissue. Rapid curing may also lead to tissue necrosis. Midwives have not noted such reactions because minimal amounts are being used for perineal repair. Nevertheless, with a greater toxic potential, over-the-counter products are inappropriate for use in wound closure.
Medical grade products currently available contain either butyl, isobutyl or octyl esters. They are bacteriostatic and painless to apply when used as directed, produce minimal thermal reaction when applied to dry skin and break down harmlessly in tissue. They are essentially inert once dry. Butyl products are rigid when dry, but provide a strong bond. Available octyl products are more flexible when dry, but produce a weaker bond
So basically normal superglue will work but with unpleasant side effects