No one can tell you over the internet what loads may or may not be safe in a given gun.
A 1932 vintage gun would be right on the cusp. For more than the previous three decades the "standard" 16-gauge shell in North America was put up in a 2 9/16 inch paper case, and carried loads of 7/8 and 1 ounce of shot, ahead of various amounts of bulk or dense smokeless powders. Longer 16-gauge shells with more/better wadding, were offered in 2 3/4, 2 7/8 and 3-inch, by the loading companies but they were never popular. When Western Cartridge Co. introduced progressive burning smokeless powders to shotgun shells with their Super-X loads in 1922, they came out as a 1 1/4 ounce load in their 12-gauge 2 3/4 inch Field shell and a 1 ounce 20-gauge load in their 2 3/4 inch Field shell. The next year, they introduced their 1 1/8 ounce 16-gauge Super-X load, but it was put up in their 2 9/16 inch Field shell. So, high velocity 1 1/8 ounce 16-gauge shells had been on the market at least nine years when the gun in question was made.
In 1931, Remington Arms Co., Inc. introduced the 16-gauge version of their Model 11 and "The Sportsman" autoloaders and they were made for 2 3/4 inch shells. Along with these guns, Remington introduced a 2 3/4 inch 16-gauge shell. While their regular 2 9/16 inch 16-gauge progressive burning powder shell, Nitro Express, came with a load of 3 drams equiv. and 1 1/8 ounces of shot, their new 16-gauge load in the 2 3/4 inch case carried a load of 3 1/4 drams equiv. and 1 1/8 ounce of shot. They called this new shell the Auto Express --
So, there is every chance that an up to date sportsman might have ordered his 1932 BH 16-gauge chambered for these new 2 3/4 inch high velocity loads. By 1938, both Winchester and Western had added these 2 3/4 inch 16-gauge loads to their Super-Speed and Super-X lines. Western even called it "magnum", but not to be confused with the "2 3/4 inch magnum" loads that were introduced in 1955 with the 16-gauge version carrying 1 1/4 ounces of shot!!
Bottom line, there is more to it than just saying "oh use light RST loads" which would be great for the clays and Quail as mentioned. Have the chambers been measured? Get a PGCA letter on the gun and see if it was ordered with a longer chamber. Is it a dainty little 0-frame 16-gauge bird gun or a heftier 1- or 2-frame waterfowl gun?