Yes- have some experience in firing old guns- and your Ithaca beauty is not old YET. 1937 was well after the era of Damascus or Twist steel barrels, and the need for black powder shells.
Where problem do arise is (a) taking Grandad's pre war shotgun, and loading it with the hottest made-last-year magnum shell, cracking a stock that had shrunk and was not tightly fitted, or (b) not realizing that a standard shell THEN may have been shorter than a standard shell now (especially for 16 g shooters)
I WOULD ask a decent shotgun smith to check the gun over, and check chamber length, insure parts, screws, and stocks were snug, bores clear- then go get a box of Dove or Trap loads, and shoot it. Old guns need love too, ya know?