MacDrive is a good option for you, but keep in mind that there is a free option, if you're willing to tinker a bit when you need to copy the files over:
You mentioned that you have your external drive formatted in a Mac format, so I'm guessing you used HFS+ (Mac OS, Journaled). Since Windows can't write to it (without that MacDrive program you mentioned), you need to get it to your Mac and then send it to the USB.
You will need an ethernet cable for this...
IMPORTANT - First, turn off (disable) your Wireless Adapter on both your PC and your Mac. If you don't, you'll confuse the hell out of your computer and this probably won't work. You didn't specify which type of Mac you are running, but as long as you're running some form of OS 10.4 or later, this should be accurate:
System Preferences -> Sharing
Turn on Windows Sharing and File Sharing in the options below. Make sure you associate an account with Windows Sharing.
System Preferences -> Network -> Built-in Ethernet
Connect an Ethernet cable from your PC to your Macintosh. Wait a few seconds, and you will get an IP address. This will be an Autoconfig Address starting with 169.x.x.x which allows you to work over INTRAnet, but you won't be able to surf the web (temporarily)
Next, on your PC machine open My Network Places. Add Network Place, and type exactly the following
\\169.x.x.x\username
and hit OK. The 169.x.x.x is obviously the IP address of your Mac listed above in the System Preferences. The username is the name of your homefolder.
For instance, if your IP address was 169.153.121.2 and your home folder was named ibook, you would type \\169.153.121.2\ibook and you should be good to go.
This will then ask you to put in a Username and Password, so just put the same as the one on your Mac.
Voila, you will be looking at your Macintosh HD. I usually make a folder called "Temporary Backup" in my Desktop Folder, and then transfer all files and folders into this.
Once the files are copied (10GB usually takes between 15-25 minutes, sometimes less), you can then just move them to your external HDD from your Mac. If you're worried about disk space on your Mac, then delete the files after you successfully transfer them.
There's an extra step in here, but if you're a cheap bastage like me and refuse to spend $50+ for MacDrive, it's a nice little workaround.
Good luck!