Honestly, the problem with a dirty bomb isn't the cancer rates or w.e, its the sheer amount of propaganda that has gone into scaring people over nuclear energy. Yes, the propaganda is mostly to stop nuclear reactors to force reliance on oil, but its still there.
I used to use a nuclear soil density gauge. The gauge was not at all scary, I could use it as a seat for a whole year, and it would have a minimal effect on my lifetime cancer rates.
But no matter how many times I explained it, as soon as I said "Nuclear Gauge" people got scared.
"Nuclear" has become a scare word, so a nuclear dirty bomb is terrifying to people.
Perhaps,
You could probably make a backpack nuke, although I don't know that Iran specifically could.
and I guess if you have a backpack nuke, you can just make it be a really bulky vest