Unfortunately this answer will be very short, but in a 4 year undergrad study (as well as 5 years of personal study) of Japan with a lot of focus on Early Modern and Modern Japanese history and what I would consider a fair amount of study on the war effort and real accounts of the war (reading diaries and last letters to family members of special attack (kamikaze) pilots) I have never seen mention of the use of such traditional masks by soldiers. Doesn’t mean it didn’t happen, but I would consider it highly unlikely.

It might be good to note that regardless of popular culture my understanding is that Japanese combatants were disciplined troops (to the point of being able to take on literal suicide missions for their country) and obviously had rules about their dress.

The most non-standard military dress items that I have heard of or read about are senninbari 千人針 or 1,000 Person Stitches, which were sashes given to soldiers. The sashes had 1,000 knots of fabric or stitches ostensibly sewn into them by 1,000 women, and were worn as good luck charms and sometimes devotional items to women on the home front.

Sorry I don’t have a more fun answer, unfortunately wartime efforts especially late in the war for the Japanese were pretty lacking in artistic flair and were quite brutal. (Women and children often trained with bamboo spears or how to correctly jump under a tank with a grenade near the end of the war to prepare for a home island invasion.)

Sources John Dower’s War Without Mercy きけ、わだつみの声 Listen to the Voices from the Sea As well as various translations by Samuel Hideo Yamashita who I had the honor of studying beneath.