If you can persuade one of the locals to take you out on a small boat, there is excellent jigging to be done, and if you like grouse, there is alsoe fine options. To hunt in greenland you will need to be with a local. I recommend a varmint rifle, as the grouse is often seen from afar. There are alsoe polar foxes, and sometimes polar hares.
If you prefer Hiking, the area is beautifull, and hardly ever has bears. Be sure to make an appointment with the locals on youre return, so they can search for you, if you should get lost, it is an extremely lonely area, hardly any people out there normally.