Landing Craft Tank (LCT) with M2 Browning 50 Cal.

am an artist working on a WWII drawing of a man’s father who was a US Navy sailor aboard LCT(5) 207 on D-Day. His name was George H. Greene and according to his son, he was firing a Browning 50 Caliber machine gun from the LCT when he was wounded in the arm.

If the LCT's standard 20mm Oerlikon guns were replaced with M2 Browning's, would they be the standard variant or the Naval variant with the water jacket?

 

Almost certainly the M2HB (air-cooled with heavy barrel, as seen in your first picture). Water-cooled .50 cal Brownings (M1921 model) were uncommon during WW2.