Elemental recomposition skill = the ability to mold one's chakra towards a certain element. Every ninja has at least one element that their chakra naturally molds to, called their affinity. Minato designed the rasengan so that he could mold his chakra into an element that came naturally to him, or his affinity, and mold that chakra into the rasengan to gain its elemental variant. Why can't you accept that?
And, again, you stated that he had no elemental affinities. Which, as I stated, encompasses from a single element to all elements. The fact that you are backpedalling because I called you out, and stating you only meant more than one elemental affinity, shows desperation on your part.