I solved it! Solution was, wire both black (hot) wires from the fan to the red (hot) wire of the new USB cable I used to make the splice. Then, wire the two white (ground) wires from the fan to the black (ground) wire of the splice. The green and white data wires on the new usb are dummies, they don't connect to anything. Once I figured that out, the rest was - hard! Dealing with such small wires is anything but easy.
This is how you have to do it, if you wire it wrong bad things could happen. You can't use the data wires on your replacement usb, they are not power wires. Only the #1 connector on a usb cable is a power wire. The #4 connector is neutral; #3 is data positive, and #2 is data negative. But you don't use 2 and 3 in this case, as no data is being transmitted.
The usual colors of these wires is: 1=red, 2=white, 3=green, 4=black. On my Targus cooling pad fan, there two black and two white wires, corresponding to positive and negative. So I just wired the two black wires together and then wired them to the red wire on the spliced usb cable. And the two white wires I wired together and then wired them to the black wire on the spliced usb cable.
So there it is, case closed. Unless it blows up. but I'm pretty sure I did it correctly.