No person shall hunt for, pursue, trap, capture, kill or destroy by any means whatever, or attempt to trap, capture, kill or destroy by any means whatever, any animal commonly known as deer, moose, elk, caribou, badger, beaver or muskrat, or any bird commonly known as pheasant, grouse, partridge or swan, in or within 2 miles from any public park belonging to city and containing over 200 acres of which 150 acres or more is woodland: Provided, This section shall not apply to any act done in any public park by the superintendent, keeper or custodian thereof.