In reply to graham F:
Was about to suggest this. If you fly into Geneva, why go to the North side of the mountains at all? Just take the train up the Rhone valley almost to the end, and hike in from Fiesch, up the Aletsch glacier and across Grünhornlücke to the Finsteraarhorn hut in one hard day.
Alternatively, take the bus up to the Grimsel pass, and hike up the glacier to Oberaarjochhütte. If the weather is good I would recommend climbing Oberaarhorn next morning before breakfast, watch the sun rise from the summit (fantastic views of Schreckhorn, Lauteraarhorn, and Finsteraarhorn NE pillar), and head back down to grab a lateish breakfast at the hut (ask the warden the day before whether this is possible, usually depends on how many people are hiking out to the Grimsel and therefore want a late start anyway).
At 3400ish meters Oberaarhorn is a perfect easy summit for acclimatization. Next day, walk across to Finsteraarhorn hut, best taking the long way round as the direct way via Gemschlicke is probably a rockfall death trap in the current heat wave. Then Finsteraarhorn, and out to Fiesch via Grünhornlücke / Aletsch glacier. I can also recommend Gross Wannenhorn as an extra summit from Finsteraarhorn hut. A few years ago we had the entire mountain for ourselves, with the hordes all going off towards Finsteraarhorn, the Fiescherhörner, and Grünhornlücke.
CB
Sorry, missed the no huts bit. I am sure you would find space to camp/bivy on the way in from the East, I just wouldn´t stay directly above the huts where they get their drinking water.
Post edited at 13:36