A rather unusual question

[Sunray]

"...sergeant major in the Luftwaffe..." German Para's were Luftwaffe controlled, not Wehrmacht. Any individual service records are long gone. The best you can do is research the 1st Para Division's movements.
1st German Para Div. were a formidable bunch and highly respected. Tangled with Canadians in Italy, regularly. They lost, but not without doing what they were told to do. Your grandpa must have been moved around a lot. The 1st German Para Div. ended the war in Italy.
This is Wikipeda, hence unreliable, but it's a bit. 1st Parachute Division (Germany) - Wikipedia, the free encyclopedia