WI: Neville Chamberlain dies earlier?

In November 1940, Neville Chamberlain, the former PM of the United Kingdom, died of cancer following his resignation in favour of Winston Churchill earlier that same year.

My question is what might have happened in the event of Chamberlain's death prior to the outbreak of the Second World War? Appeasement isn't likely to change, of course, but the change in Prime Minister in 1938 or 1939 could have widespread ramifications.

What might these have been?

(Note: the year in which he dies is down to you, as there are many scenarios we could explore based on the different possible years.)
On the whole, likely not much change to strategy given that his likely successors were either Halifax or Hoare who agreed with Chamberlain's realist Germany policy. Eden was too young and too hawkish to feasibly win the Premiership if Chamberlain dies in early 1938 whilst Churchill was a joke at the time.

So, if Halifax or Hoare, history still takes a broadly similar course but hinges on how they deal with the German peace deal and what happens when Hitler breaks it