You can't pick it up with a forklift to put it inside the sealed container. That would make the forklift (and its operator) radioactive. You can only use a forklift after it's already within the sealed container. See for instance this real-life video (shot on a nuclear power station in my country), which shows used nuclear fuel rods being put inside a sealed container for long-term storage: https://www.youtube.com/watch?v=7X5K46ALdD0
Anyway, the forklift example wasn't about literally picking up pieces nuclear fuel with a forklift. You obviously use the forklift to move the shielded container around which contains the nuclear waste. Nuclear fuel in general is always at least in a water bath, which shields the neutrons, so your forklift is going to be fine.
In contrast to nuclar fuel, you cannot use a forklift (or any other equipment) to feasibly pick out the evenly mixed mercury atoms from the ocean or the atmosphere that we put there from burning coal.
aka the solution to pollution is magmatic delusion err... dilution.