In reply to laraichean:
I've done loads of Alpine hut to hut routes and most have a fair bit of ascent and I agree in your situation Alta Vias etc may be too demanding.
I've always found Ken Reynolds Trekking/Walking in the Alps as excellent starting point for deciding which ones to do.
I think part of the Tour de Vanoise would fit the bill. We did this a few years ago and the ascents and descents are certainly easier than say the classic routes in other parts of the Alps - but still in great Alpine country, so certainly not a Sunday stroll.
The huts were welcoming and a pleasant surprise for the French Alps is that they stocked beer from local micro-breweries!
We flew in to Milan and got the train to Modane where we started and finished but no reason why you can't drive from Geneva. I produced a plan which shows each day start & finish plus ascent & descent (based on the Cicerone guide).
You could pick a few days of this, maybe starting & finishing at a different place.
If you are interested, email me and I could send you the plan.
Separately, I also have similar plans for other hut-to-huts, including off-route mountains, we've done throughout the Alps, so contact me if you're thinking of another area.