You can't rely on the integrity of the ground/earth on the pipework of the sink. For all you know it could be connected to PVC pipework further down. In the U.K all pipework is meant to be cross-bonded which is then taken to the earthing bar. However in Japan I am unsure if this is what is done. Regardless you should be earthing/grounding it back to the incoming supply.
In a lot of countries that use two pronged devices they are actually fed from centre-tapped transformers or are double insulated devices. Either way they should not become dangerously live.
In short don't connect to the sink run it back to the earthing/grounding bar.
You must always follow the most recently adopted code when installing new wiring, no matter how old the house is. With that said, the cord of a cord-and-plug attached device is beyond the scope of the National Electrical Code (NEC).
Installing a new range
When you purchase a range, they will also sell you the attachment plug. If you opt to install the stove yourself, they will ask you if you need 3 or 4 wire. This is because if you already have a 3 wire receptacle that was installed before the code change then you are not required to update the house wiring when installing the range.
When you're ready to install the range in the house, you'll follow the manufacturers installation instruction for a 3 wire attachment plug. Once the cord is attached to the device, simply plug it in and you're done.
Installing or modifying a range circuit
If you are installing a new circuit for the range (which it sounds like you might be), or modifying the existing range circuit, you must follow all currently adopted codes. This will likely mean running 4 conductor wire, and installing a 4 wire receptacle. Remember, the code is applied during installation, not when the materials are purchased.
Side Note: Technically, code applies at the time of inspection. However, the inspector will usually use the date the permit was granted. So if there was a code change after the permit was pulled, but before the inspection, the inspector will usually use the old code.
If your range has a 3 wire attachment plug, you'll have to follow the manufacturers installation instructions to change to a 4 wire plug.
Best Answer
What you need to do is replace the cord with a proper cord and install a US compatible plug of the proper voltage and amperage. Assuming this appliance is 120V, it should be plugged into a GFI protected receptacle. DO NOT just cut off or ignore the ground wire.