Like yourself, after paying for an external contractor coming in and supplying unsatisfactory results I got permission and the company to purchase a TX200 Mk3, scope and lamping equipment to cater for the ferals both outside and inside the premises.
Luckily I am the H&S Manager so I was deemed competent to create both the risk assessment and Method statement, I was also in a position to negotiate with one of the national pest control companies to attend their air rifle marksman course with another employee, which incorporates the legislation and methods of dispatch and carcass destruction