I think there were no problem hunting on Elm Park. Never heard of any decree or rules that prohibited hunting on Elm Park.
Check this few interesting facts of Elm Park quoted on there website;
March 1854, Elm Park was purchased as a "new common," putting the city, together with Hartford and New York, at the forefront of the urban parks movement in the United States.
The "Commission of Public Grounds" that was appointed in 1863 did almost nothing for 7 years. Its most significant act was probably naming the "new common" Elm Park. Twice it pleaded for a $10,000 donation to properly drain the 28 acres of lowland. The commission raised money by selling hay and apples from the undeveloped park, renting it to the agricultural society, to circuses and caravans, and to farmers for pasture.
Upon becoming the head of the Parks Commission in 1870, Edward Winslow Lincoln found he had little to rule. At that time Worcester's parkland consisted of an "unsightly" eight-acre Common and a larger twenty acre tract known as Elm Park.
Elm Park primarily served as a dumping ground for the Highway Department... "[and] the casual job-wagon or wheelbarrow."
In 1875 Commissioner, Lincoln, had become seemingly annoyed with the negative impact of circuses on Elm park. He lobbied the commission to pass an ordinance banishing them permanently from the park.
In 1876, Lincoln petitioned for police patrol of the park, declaring, "this Commission will exact and enforce that decent behavior from all who frequent the Public Grounds, which is not only seemly in but is rightfully expected by the community."
In January 1884, 231 members of Worcester's west-side elite, petitioned the City Council to purchase Newton Hill, a sixty acre tract adjoining Elm Park. Their motivation, however, was not entirely aesthetic or recreational. They also saw Newton Hill as an ideal spot for a reservoir that would provide fire protection for their fashionable West Side homes. Pressure by a retaliatory east side "working class" group thwarted their effort, and caused their petition to be put on hold. A revenge tactic stemmed from the earlier defeat of their own efforts to secure parkland for their constituents.