In reply to JXM:
Go to the Marco e Rosa - it doesn’t take long from the summit, couple of hours perhaps at a gentle pace. You can stay there and do the Piz Palu traverse the next day. Nice little scramble up followed by a beautiful snow ridge and easy glacier descent as long as the holes are covered up. It’s a short day and you can link it into a single day if you’re fast but the Marco e Rosa is a nice enough hut and at over 3,500m it could be great acclimatisation for a bigger 4,000er.
That gets you to the Diavolezza (?) cable car or you can walk down if your knees are holding out! Either way, you get down to the road where you can either hitch or get the train back to Pontresina (seem to recall the train was about CHF 10).
Finding somewhere to park for 3 days in Pontresina was a challenge. My mate left his minivan in a hotel car park - how he didn’t get clamped or towed, I’ve no idea!
Oh and if you don’t leave the hut walk in till late afternoon like we did, you can get a horse drawn carriage to take you and/or your luggage on the long, flat walk in to the half way(ish) hotel. I think luggage is only about CHF 5 - I’d pay it even though they take it to the hotel which is perhaps a 10 minute detour from the path to the hut. It’s a nice walk though, even with no equine assistance!
The Biancograt struck me as a route which is nicer to look at than climb - don’t get me wrong, it’s a nice enough route but when you’re on it, it doesn’t feel as stunning as it does from the hut! In some ways I actually enjoyed the Piz Palu traverse more. Both well worth doing.
We took half a set of nuts and cams but didn’t use any of it as there are a few bolts in the rocky sections and the rock is often fairly blank anyway (and chossy in places). Worth taking a few pieces just in case but keep it light. There are some abseils on the descent so you do need a rope even if you choose to solo most of it. Can’t remember how long - we would have had a standard 60m rope.