Plug in Cams

Hello, does anyone know how long the outdoor plug in security cams wire is? The reason I am asking is that I want to get the electric to power the plug in from my existing outdoor lights. I am going to use one of those light bulb plugs and plug the cam right into that. I just need a very short wire from the cam since I will be mounting it right under my existing outdoor light fixture. If the cam only comes with a very long wire; do you think that I could cut it to the short length that I need and attach a new plug to it? Thanks.