Definately shouldn't run it off the motherboard as you've said.
12V x 1.6A = 19.2W (most fans are like 2W)
So yeah, you need to get a female molex connector, and wire it in. This will not give you fan control, and it will run at 3900rpm all the time until someone you live with stabs it with a screwdriver (unless this is going in a server rack, in which case, party it up, our server rack sounds like a tornado 24/7).
Cut off the 5 pin plug, strip wire, and connect to the molex however your female connector is used. From memory you solder it to the pins, then the pins get clipped in to the plug.
You could however wire the negative to the +5 pin. This gives 7V and probably a more reasonable rpm range. Might be worth experimenting.
Edit: you said 'tape it to a molex is the last step' - do not tape it, even if you join wires rather than buying a female molex, they should be twisted, soldered, and heatshrunk (or at least electrical tape). If you can't solder, find someone that does. Wind and tape will work, until it comes loose in a few months and shorts on the case. You could also use a 'chocolate block' or terminal strip (whatever they call it where you live). This still isn't great, but I prefer it to twist and tape.