Then later, Satoshi contacted others for input that contributed to the whitepaper (Wai and others)
Don't think so. Satoshi cited prior work that he used, but I'm not aware there was direct contact/input from those people.
After the whitepaper was released, one other individual came along to help Satoshi build the software (Sirius).
So Satoshi did not code. The existing pieces wisely joined together. Satoshi said what he had to do and put out the idea. Later, programmers adopting this idea undertook the task of coding. Is it correct?
Not what I remember about this. The code for the original Bitcoin 0.1 prototype was structured in a way that made certain modifications to the code more difficult, and this has always been attributed to Satoshi's programming inexperience. Satoshi got coding help for version 0.2, but not for the 0.1 original AFAIK