<map lat='71.16410288637437' lng='25.791263580322266' zoom='12' view='0' float='right'/>
Once you have reached Nordkapp, your best bet to hitch out (which involves you return back from where you came) is to hitch a ride at the NordKapp Interpretation Centre itself. You should at least manage to get a ride to the nearest settlements of Honingsvag or with luck even manage to get out of Magerøya Island.
Anyhow, the distances are so big that walking out of the place is basically useless since Nordkapp is anyway the emission zone of all traffic in the area. The same applies when it comes to leave the island while hitching from Honingsvag, it is better to stay at the crossroad of the E69 at the entrance of the town instead of walking along the road and into any of the 4km+ tunnels.
There is two things to bear in mind, the Tunnel to Magerøya Island is toll per passenger in the car (both ways). You might therefore have to pay your due. After the Tunnel, the only worth ride to catch is at least until the crossroad of the E6.