A very interesting idea; I would think that initially there would be very little impact. Particularly with radio communication and at least some better understanding of volcanology it is doubtful if the ILN would have had any major units close enough to be seriously impacted. Any land units on the island or nearby would have had ample warning. The greatest destruction, apart from Krakatau and nearby islands was on the coast of Sumatra which was not very strategic during the war. Japan was evaluating New Georgia Island at the time but basically New Guinea was between New Georgia and Krakatau so no tidal wave (to use the 1943 term).
The longer term impact would have been through the impact on weather. Longer colder winters in 1943-1944 and 1944-1945 would have impacted the European Theater. A longer winter would have delayed the red Army’s June 1944 offensive but probably by only a few weeks. Weather impacts could have made the Battle of the Bulge a much different affair; although both sides would have been impacted. Food production would have taken a real hit. United States production would have remained sufficient to sustain the US Army and Britain, although perhaps at slightly lower caloric levels. Occupied Europe would have been really bad.