Not saying it was 100% impossible that he COULD have fought in WW2, but it didn't happen, according to his bio once again in wikipedia
" Rogers was born on March 20, 1928, in Latrobe, Pennsylvania, about 40 miles (64 km) outside of Pittsburgh, at 705 Main Street[1] to James and Nancy Rogers. James was "a very successful businessman"[2] who was president of the McFeely Brick Company, one of Latrobe's largest businesses. " https://en.wikipedia.org/wiki/Fred_Rogers
He wasn't an urchin who needed any sort of paycheck to survive, he was born to an upper middle class family and didn't secretly enlist into the war effort in his teens and rise up in the ranks to lead troops then return to highschool to take that picture. As much as I would like to believe Mr. Rogers killed dirty Nazis (and as much as I would love to see them all dead even the ones who are polluting the world to this day), it didn't happen