A cotton ball is a nice way to clean the cord too. The benefits of the cotton ball are that it holds more of your cleaning solution. If you're unsure of which to use, you can always use both. You can either switch off at each cleaning or use both each time.
The cotton ball is handy if you're leery of cleaning deeply, because you can drip lots of the cleaning solution into the area of the umbilical cord.
Photo © Robin Elise Weiss