A probably stolen game radioactive waste item is inventory rather than a fixed location or an event, and it takes up storage space until you get rid of it. The normal route is the same trip you already make for scavenging: carry it to the dumping grounds in a backpack and use the hand-off.
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Probably Stolen game radioactive waste: the normal route
Put the waste in a backpack.
A light or a heavy pack both work.
Travel to the dumping grounds.
Use the hand-off or drop-off interaction.
Keep spare inventory capacity.
The item can come back and the trigger is not something you control.
Recheck your inventory afterwards.
Rather than assuming the disposal took.
The same trip is where you pick up scrap for the furnace, and it costs you the morning you open — the night scavenging guide covers the trip order, the wound odds and what you can bring back.
The container fallback
For later in a run, or when you cannot make the trip:
Select a storage container you can afford to lose.
An empty Security Crate is the reported example.
Put the radioactive waste inside it.
Put the entire container in the trash.
That disposes of the waste and the container in one action, which makes it an expensive alternative rather than a free one.
What does not clear it
Handing the item to Security is not a dependable disposal route — players have reported Security becoming angry rather than accepting it. A machine that would store the waste and convert it to energy is not part of the build.
Selling the item is a gamble rather than a plan. Treat it as storage you want back, not as stock you want to move.