Adhesive/Glue to Use on a Laptop Power Supply Cord Repair???

So the wire insulation on my laptop power supply has cracked and broken and is now separated from the power supply itself just a little bit so that I can see the internal wires. They have not broken and the power supply is still totally usable. I want to know what kind of glue/adhesive I can use to keep it together to prevent further damage from occurring. I've heard before that super glue or krazy glue will cause damage because the cord insulation is PVC and the glue will cause a reaction with the cord and the bond will not hold. (although it seems like a rubber compound to me). Can someone suggest what I should be using to bond this back together?? Thanks.