I've never used a disk wiper, so I can't personally recommend one, but you should easily be able to find one by googling on some combination of 'wipe shred free space review,' and seeing which ones are rated highly by users, PC magazines, etc. Almost all disk utility suites by companies like Symantec, Paragon, Acronis, etc. contain this function, and there are several freeware or shareware utilities as well. You might also look into TrueCrypt, which is a free disk encryption program that can encrypt entire partitions, both data and free space, with algorithms that nobody short of the NSA could break. I do use and recommend TrueCrypt, but BE SURE to read the entire manual first. You can skip the parts about hidden partitions and files --- they are overkill IMO.
If you are in a huge hurry, I would do this:
First, empty your recycle bin, so that Windows will not try to preserve deleted files.
Next, take a DVD of your favorite movie, or your windows install DVD, or any huge file you happen to have lying around, and copy it to the partition you want wiped. Repeat with other big files until you have no free space left. Then delete all those files you just copied, empty the recycle bin again, defrag your partiton, and repeat the whole process as many times as you need to feel safe.
Filling the partition just once with something innocuous will be enough to overwrite the free space well enough to keep anyone you are likely to know from seeing anything; twice should be good enough to beat anyone short of the FBI.
Also, if you don't even want the filenames to be seen, as opposed to their contents, you should be aware that the filenames might turn up in all kinds of places on your system partition --- paging files, hibernation files, the registry, favorites lists, shortcut lists, recently used items list, etc. Since you don't sound like an expert, the best way to purge all of that is to reinstall windows, preferably on a new drive, and wipe your old system partition as above.
Hope this helps.