Halifax, actually, would not make peace with Germany in spite of his poor repuation in the Chamberlain government. He might not make the giant rousing speeches that Churchill did, but I think that Halifax would probably let the armed forces fight their own war as much as they could; you could then justify "Operation Compass Succeeds" ITTL as a great triumph and the start of the UK getting back into the game.
Then, with North Africa failing and Germany's attempts to reinforce the region coming to nothing, the UK has more forces for Singapore, which might be enough for even Percival to win with. I don't think Halifax would send force Z to the Far East; frankly, I think Halifax would be good at the silent act of governance--the making deals and brokering with allies. OTL, however, he had a lot of trouble getting along with the United States, and that could be a major factor. That might simply mean that there is no Atlantic Charter and that Halifax-FDR meetings don't happen as much or at all like FDR-Churchill Meetings.
Hey, if Halifax wins WW2 for Britian, he easily redeems himself from the stains of Munich to become a great hero. The Greatest, even...