Just chiming in as a local that the area is frequented by not just ships with professional equipment and captained by professionals but also by many locals out for a quick fishing trip, leisurely drive, or, in rare cases, quick trips using small fast craft. These are unlikely to notice a single swimmer with no marker.
(As an aside, the sides of Litle Hjartøya are in many places too steep to get out of the water without climbing. I can't recall this exact area, but I believe most of that side of the island is sheer rock.)
A much more sensible option would be to rent a small boat in Bodø, or to charter someone to take you there and back again. If you have some time you could advertise in the regional newspaper, or if you are in the region I would simply ask around the harbour.
If you're instead looking for a swimming challenge there are plenty of beautiful areas with or without small islands in the vicinity:
- Mjelle, a popular swimming and leisure spot.
- Sørfjorden in Mistfjorden, part of the new Sjunkhatten national park.
- Vatnvatnet, except for the north-eastern arm marked "Heggmoen skytefelt", an army training ground.
Another option would be to take the "hurtigbåten" to any of several islands nearby.