Crankshaft pulley question

[marty in Ohio]

I'm reading about the difference in a one piece pulley vs. a two piece pulley. The two piece can be removed without taking the radiator out? I assume the two piece can only be initially installed with the engine or the radiator out. Am I right? A friend is afraid his pulley is wobbling and we don't know which pulley he has. We have access to the "special wrench" but not sure there really is a problem. How can we tell which pulley we are looking at?
Marty