In reply to chenav:
Some more info: I'm looking at late June 2024, once the refuges open but snow conditions are still good and trails are empty.
Could do a 3-day tour from Saas Fee, with two overnights in Britannia Hütte, combining some rock climbing on the Egginer on the first day en route to the hut, climbing Rimpfischhorn as the main course on the second day, and finishing on Allalinhorn via Hohlaubgrat - and maybe Alphubel if we're up to it?? - on the final day.
For the start of the week perhaps Dent du Géant and Arête de Rochefort, obviously staying at the Torino Hut for some warm-up climbs the day before - and of course to start off acclimatization for the week ahead. Though this is just one idea, there are lots of possible two- or three-day warm-up programs in the area with similar technical challenges.
All guided, as mentioned above.