I haven't programmed a key, but I have done similar. I have programmed a second hand fob to ma hippo with me hawkeye and it worked. I have also taken ma hippo's working key and working fob, then disabled them with me hawkleye, independently. They stopped working so I then enabled them with me hawkeye. This is slightly different to programming as yer disabling a "known to the vehicle" device from within the vehicles computer. Essentially telling it to ignore a known device.
My advice to the OP would be to have a go and follow the menu on the hawkeye. Unfortunately they don't produce guides to take you through such situations. I have done a number of vid's on me you tube channel on the hawkeye but not this. I did film it but not sure where it is as I have hours and hours of this stuff mixed in with other diagnostic stuff.
If yer go into the programming option just follow the instructions. It will give you a warning about being able/trained to do it etc... keep going. I think you will need a working key to be able to program a new key. In fact I'm certain this is how it's done, but it's been a while. By working key I refer to a key which will key unlock a locked hippo, and key start the engine via turning the ignition, on the hippo. I would also advise the hippo be in a location where you can get to it with a tow truck in case it goes wrong and you need to recover it to a garage.
