I'm unsure what you mean by kokyu-nage. If it is the same as sokumen irimi-nage (side entering throw), then it is very similar. In fact the gradation from irimi-nage, kokyu-nage (side-entering) andkokyu-nage (just on the arm) is just a matter of where you are in relation to uke (and how far uke turns towards you) but are all basically the same throw.
I always think of irimi-nage, kokyu-nage and ikkyo forming three core techniques in aikido - partly because irimi-nage and kokyu-nage are similar, but are just responses to a different reaction from uke or a different position between you and uke. The reason ikkyo is part of this trio is because if you do irimi-nage or kokyu-nage and uke puts up an arm to defend themselves (e.g. from a potential blow) that allows you to do ikkyo.
Isn't aikido amazing?