You park the forklift in the storage container and seal it in. It's not that hard.
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.