I like these sorts of hacks.
So you have an adapter, I am guessing it draws all the power it needs from the USB.
Unlike a lot of the ones I have seen (which come as part of the adapter) you have been given a wall socket to molex power adapter (and then a molex to sata adapter).
I also have to assume it is 700mA at 12V aka 8.4W and furthermore I do not know the load balance between the different voltages.
Standard molex/ata as you say is just 5V and 12V
http://pinouts.ru/Power/BigPower_pinout.shtml
Sata is 3.3V, 5V and 12V (naturally all DC).
http://pinouts.ru/Power/sata-power_pinout.shtml
Easiest way and rather crude is the poor man's socket doubler, here you cut into the wall facing side (before the transformer on each) and solder like wires to each other, I am not sure of Italian/continent wiring colours right now and even then I would be inclined to still test the pins match rather than relying on colours (manufacturers are not to be relied upon as my several of my of shocks will attest) but is a simple thing so no worries there.
I do not think the fuses are anywhere near the limits with the wii and drive transformer but it might be worth a check.
Nicely your adapter appears to use a "kettle" (standard PC) lead meaning you could probably scrounge one up from somewhere.
Next we go into proper electronics.
The obvious place to start is a power source that is certain to be there, now the wii has two external USB ports although one looks to be powering your drive (maybe still available if you are up for a bit of splicing).
More on USB power:
http://www.girr.org/mac_stuff/usb_stuff.html
http://pinouts.ru/Slots/USB_pinout.shtml
Note that while the limits are fairly high (500mA per hub*) in the spec there is a initial current draw limit of 100mA, many USB implementations ignore this but some do not. I have no idea where the wii exists with regards to such things. Short of proper electronics any device would be very crude and not identify itself and so not conform to the current limit requirements.
*not sure if each port counts as a hub, either way between the adapter and the drive even split between the two it is are pushing limits if you are not already beyond them and I would not do it.
In addition to all of this you would still need a 12V source and running an inverter for such low levels does not sit right with me.
Next up with the wii output.
I have not got one to hand right now but according to this site:
http://www.gamebay.com/Original_Nintendo_W....htm?click=1913
"Output : DC 12V 3.7A" which I am going to go with until something better comes along.
First up I have no idea how close the wii pushes this supply and "hacking" a transformer is something I do not suggest doing unless you know how they work through and through. 700mA is not play power either, the standard overhead for such things is often quite high but I doubt this can take a 700mA hit and even if it could you would need to test it under load (not just idling on the menu).
Immediately though you should notice 12V which fits one part of the requirements.
If you were to try and power it from wii hardware I would consider splitting the device between USB and wii power (I know it sounds a bit like circular logic having just counselled you against trying to draw too much power but that 12V*3.7A also accounts for the USB down the line). Get a multimeter and does the maths though as I am not confident it would work at all without external power.
Speaking of external power most TVs and other devices around it can spare some if you are up for making an octopus of wire.
In short go with the cheapo socket doubler.