Could Germany and Italy support useful independent fleet deployments to a Far East war, or exploit the distraction in Europe?
Short answerTheir Far East deployments would depend on allied bases and support, while Germany in January 1939 was unprepared for a western offensive.
NotesThe counterfactual has a practical naval constraint: German or Italian ships could appear only as supported pieces of an allied task group. Germany would probably send a fast capital ship once one became available and avoid exposing a Deutschland-class ship. Its forces were still reorganizing in January 1939, which made a western offensive a poor way to exploit Britain's distraction. In this reading, the later Phoney War reflected a wider lack of readiness among the European belligerents.