A lot of places don't do one night only accommodations. So if you see anything at all for one night, snap it up now.
Yes, it's more expensive that way I think. But cheaper if you go on a ship other than the catamaran from Hamburg (the ship from Büsum).
You'll love Helgoland. My tip: upon arrival, do the bunker tour, even if it isn't available in English. Most of the local guides and other tourists will help with at least the big ideas, and it is WELL worth it. Then walk down to the beach. As the tourists start filtering toward the ferries to depart, head into town to explore the village and find a place for dinner. Then at sunset walk around the top of the island at sunset. Alternatively, do this first thing in the morning. Then when the day trippers arrive the next day at lunch, head over to the other island (Düne) and do a lap, looking at the seals. That will fill the time pretty effectively, and you will have seen most of what there is.