If James Stanhope had remained First Lord

How long would James Stanhope have remained First Lord if Churchill had not taken over?

Probably until Chamberlain's fall in May 1940, with the important consequence that carrier construction likely continues without a pause.

The estimate keeps Stanhope as First Lord until the political crisis that removed Neville Chamberlain in May 1940. His continued tenure matters because he was already carrying the naval program forward and was unlikely to interrupt carrier construction. Long Admiralty experience through the 1920s and 1930s also gave him current knowledge of its people and systems.