How do I safely connect the wiring for an outdoor light to be used inside to a stripped extension cord that can be plugged into an outlet?

You can't. If you did do it as safely as possible, it still would not be UL listed for cord-and-plug use (which is exactly what you would be doing). In short, if your home burned down due to this contraption, your insurance would not pay anything because you did not use UL approved electrical fixtures. Many people do not know this and see such ideas on HGTV shows and the like. What the shows don't tell you is the consequences, and probably because they don't know what they are. I've never seen a professional electrician suggest making your own light fixture. It's usually an interior designer or similar.