But if you have never cloned a Hard Drive before, you should practice on other hardware first.
Make sure to use a static grounding band on your wrist, and wear clothing that is least prone to generate static. Wet or gel up your hair as well... so that its not 'frizzy'.
Static might not kill the HD... but the later game PCBs are very prone to static damages.
Similarly, Try dumping your own motherboard Bios first.
If this is beyond you, then have a guy who works with Building & Repairing PCs tackle it. It will be easy for them.
A note: Some of the games HD's used a laptop HD. (Killer Instinct), and you need an adapter to be able to connect them to a standard motherboard. The converters Ive seen, can easily be put on backwards.. which would probably fry things. You have to make sure where Pin 1 goes by looking over the cable, and then find it on the HD.
Its possible to get acceptable shipping through some companies. Pilot-Air I believe charges $300 one way. However, Shipping a game is risky... especially if the carrier is careless... like American Van Lines. They have ruined $4000 pinball machines frequently from what Ive heard, and seen.