I bought a power cable for my A1176 Mac Minis, but I was a bit dumb and didn't realize that it didn't come with the actual part that plugs in to the wall. Will something like this work? If not, is there anywhere I can find one that will work or would I have to purchase a new cable?
Yep, that cable you linked to will work. If you can find one somewhere (they are also used with other AC adapters, eg for some laptops) that will also work.
Those cables are more technically known as 'Mickey Mouse' power cables. 'Mickey Mouse' for the type of plug. And yeah, any cable of this type will work with anything that has that plug type. It's an industry standard plug.