Is it possible to blink an LED with just a USB data cable and a transistor?
No, you can't do this. You need a chip of some sort to translate the USB commands into whatever you want to do. It could be an Arduino running your code, but there are also dedicated chips (like this one - note that I haven't tried this chip).

If you're trying to find parts to turn a plain wire on and off, the key word to search for is "GPIO" (stands for General Purpose Input/Output). I found the above chip by searching for "USB to GPIO".

It's not necessarily worthwhile though. In my experience, getting your computer to work with these sorts of devices is fiddly at best. If you have a working Arduino setup then I would stick with that.