One of the two wires on my small white Christmas lights broke off at the male plug (which has a fuse and is non-polarized). It broke right against the plug so I can't strip each side of the broken wire and wrap them together. I have two questions; I can not find a non-polarized replacement plug that is meant for Christmas lights. Do they exist? If not, how do I use the replacement "vampire" type clip (which is polarized) if I don't know which of the two wires is hot? There is no marking or ridges on either wire. I can make this string my end string (since the polarized plugs I've seen do not allow you to plug in another string) but I want to make sure there is no issue with polarity and that I won't ruin the string of lights (and the strings behind it) and/or the outlet I will plug it into. Thanks
Because the original plug is non-polarized and can be plugged in either way, you can just use a polarized plug. It just limits you to plugging in one way.
The more important issue is the fuse. Because the lights were provided with a fuse, we have to assume it is unsafe to omit it. It is certainly against the electrical code to omit it.
You can buy an in-line fuse holder and splice it into the (now) hot wire, right next to the plug. Just make sure to get the same amperage fuse (rated to at least mains voltage).
Do you have another set of lights you're willing to sacrifice? (Maybe that old strand with lots of burnt out bulbs that's been cluttering your decoration box for years?) You can transplant the plug from one strand to another.
Please make quality wire splices. Don't just twist and tape. I recommend making lineman's splices and adding solder and heat shrink tubing. The lineman's splice isn't ideal for stranded wire, but it'll be okay once it's soldered. The important part is that it holds the wires in place while you solder them, and it doesn't result in any large lumps that would get in the way of the heat shrink tubing.
The other important step is to make sure the plug has the right size of fuse for the lights you're using.