Strangely, the Honda manual tells one how to remove the recoil starter unit and use an emergency cord but not how to replace the cord on the recoil starter itself - is this self evident when you remove the recoil unit?
I've never worked on the Honda 2.3 but all the cord-starting engines, including my Suzuki, that I have worked on have been fairly easy to reassemble. The only issue has ever been how much to pre-tension the recoil spring but trial and error will soon sort that out.
I have not worked on a Honda 2.3 either so I am just as unqualified as richard S to offer advice
But be aware that springs have pretty sharp edges so sturdy gloves are advised
If you can a avoid releasing the spring do so. Given half a chance they leap out of their housing like a caged tiger.