Hi Claude,
Welcome to the forum.
I've never tried doing this so I'm no expert.
Does your existing flywheel have a "starter ring"?
Meaning: does it have the teeth needed for a starter motor pinion gear to engage and turn the flywheel?
The parts illustration shows the pull start only flywheel...
...(Part# 31110-ZY1-000ZA) ...
....as having a starter ring and it might work with an electric starter, as is, if you wire up a start switch and relay.
If so, maybe you don't need to change it out. If you already have a starter, you might want to see if you can fit it up to work.
I say that because I don't think that the electric start flywheel....
.....(part# 31110-ZY1-800ZA)....
....would work with your existing charge and exciter coils.
That flywheel only works with the 12 amp charge coil assembly to my knowledge.
Additionally, I don't think that your 15 hp engine has the necessary mounting holes to secure the 12 amp charge coil to accommodate a "complete refit".
Just telling you the way I see it.
I could be wrong.....often am.
Good luck.