What do you mean by the 'Iron Cross'? The term really refers to a German military decoration, which is not particular to the Nazis, it was in use a century before them, even if abolished after WWII.

Or are you referring to the black-on-white cross of the Teutonic Order, which the Iron Cross was an example of? Because that goes back to the aforementioned medieval order, and is still the symbol of the German Army (Bundeswehr) to this day.

Or do you just mean the Cross pattée shape that the Iron Cross had? Because that was not specific to the Iron Cross in the least, it's been used in many contexts for many different things, by many different countries, including on French and British orders and medals.

The swastika was not in broad use like that; the idea of it as a 'Germanic' symbol only dates back to the Vöklisch movement a few decades before the Nazis, and the Nazi movement basically supplanted them. Thus, it was the logo of the Nazis and in a German context its use as a Nazi symbol made it far more associated with them than anything else.