The "spool" lights that you are referring to were set up with that in mind. They have the cut lines printed on the casing and the splice points at those areas are set up to receive the end caps used to supply power. The lights that you bought at Walmart were not designed to be cut. While they are similar in their internal wiring, they don't have any splice points within the string and could prove to be very difficult to get power supplied to the cut end.
You would probably need to use use "old power cords" here because I doubt that the termiator kits would work with these rope lights. The problem is that this is probably going to result in a sloppy not well insulated connection. Since you will be working with 120V, I suggest that you do it the right way and get the right strings and terminators. If you really want to do this then you need to count the lights in the string (inside the rope casing). When you get a number, post it and we will take a shot at it but unless the box tells you what the voltage of the lights inside the casing are, all we can do is take a guess.