As someone who has climbed all those peaks, I haven't been up Swiss and a few others, but all the main ones, yup; you will literally be walking over manay peaks points on E-W ridge to get to Challenger and several others along the way. You won't be Bivying on top of Luna either. Top of Luna peak, some say is actually class 4, I digress and say class 3. Its sharp and pointy even though its West ridge is gentle. It is shattered large rock up there and ain't a flat spot to be had unless you like serious sufferage.
Hey, I have been in there solo. Not a big deal. I still took a rapel rope though(6mm). Its easy to get off track, especially in unfavorable weather conditions. If sunny, no I doubt you would, though others have... Yes, you can futz around for half of forever figuring out how to get past said cliff bands, but its far faster unless you already know how to get past said cliff bands, to just rapel. Assuming you can see the bottom. As I have said before, you can get through the pickets without a rope and rapeling. The original party did after all. Just do not expect to go all the places one reads about without said rope.
PS. IMO The more interesting parts of the pickets are available to those with a rope though.
PPS. Azure lake may be possible from the East and maybe west... Otherwise check a topo map. My recollection is its ringed by cliffs and parts of cliffs on top of more cliff bands.
PPPS. Whatcom peak is way out of your way from E-W ridge. If you really want Whatcom, go in via little Beaver, to Whatcom pass, climb Whatcom, cross Challenger glacier, climb Challenger, traverse over to Luna Lake/Luna Pass Climb E. Fury, backtrack go down to Terror Lake, traverse to shoulder of McMillan, look DOWN DOWN DOWN at Azure lake, traverse out either Goodell creek or Elephant bute.
PPPPS. Challenger glacier is actually a real glacier with varied crevasse problems changing from year to year. This ain't your CA/WY/CO snowfield they call a glacier. You can bypass it by going down below... Haven't done it myself, but did contemplate it when I went in solo.
PPPPPS. If I wasn't sick lately and would rather spend 2 weeks in BC, I would gladly go with you.