Those Hamilton rifles were inexpensive single shots which were often given as prizes to youngsters who sold a certain number of cans of salve, or magazine subscriptions, etc. Another gun in the same category was the Quackenbush. (If you have a squeeze type nutcracker, it may have "HMQ" on it for Hiram Quackenbush. Same fellow.)
The gun has little cash value, but I am sure its sentimental value is priceless.