Could Norway have been saved? Probably not. Could the Germans have suffered heavier naval casualties? yes. Really what was needed was the Norwegians to not mobilise by post, and to be a bit more proactive, as well as the deployment of Allied troops to be a lot less chaotic and slapdash. In timelines like the superb
https://www.alternatehistory.com/fo...-hurry-up-dying-a-ww2-polish-si-story.467055/ even with the casualties the Germans take at sea, on the land it goes poorly.
And even then a defeat at Norway won't stop an Invasion of France, and the Low countries, that was going to happen, it basically HAD to happen.
As for Chamberlains rep, if he survived norway with a somewhat better reputation, the man's still getting blamed for the UK not being ready for war and if the land battle goes poorly, but the sea battle goes well, the 1st Lord WILL ensure that he's the first one to put the dagger in Chamberlains back, after all it was HIS Navy that succeeded, not Chamberlains army....