In order for the pump to work the hammer, it would, as Jim said, have to be completely reconfigured.
Those rolling blocks were often held in place during the high-pressure part of the firing cycle by a shoulder or ledge on the hammer intercepting the movement of the block.
You can see the big ledge on the hammer (10) in this exploded view of the 1869 Remington Rolling Block. It neatly nestled under the bottom of the breech block (11), and you can see from the relative dimensions that the action was pretty positively locked by the time the hammer contacted the firing pin.
This was for a much larger, more powerful cartridge, but the principle is the same.
That's why your "pump" won't open the action on your H&A. After you fire, pulling back on the pump essentially makes the action act as if you've just fired another round and there's pressure pushing back on the breech block.
In order to make it function, you'd have to create something that pushed the hammer back to at least half cock BEFORE it opened the breech block.