I don't really like Corki but I do think he should get Kog's passive, Kog should get his passive, and their identities as such (Corki's half'n'half damage and Kog's balls-deep killin') should probably make the swap too.
With that out of the way, Corki could meet an identity a little more conducive to the bomb passive (where Kog's kit is very nearly a scale of 'how close am I to the enemy?' from P to Q thru R) and Kog'maw could feel more in-place as a hybrid hypercarry who benefits from the bulk of damage builds but less so with defensive given his primarily-assault-oriented design then.
Corki should feel more like the 'Daring Bomber,' with rewards for tight fights and clutch maneuvers, instead of both having this weird awkward demand to be both long and close range to operate at full efficiency (or else to never get use of their passive). Their kits wouldn't even need much adjustment; some care, analysis and testing would probably put both at a far more interesting juncture than either has ever known.
Package can even stay, so can Kog's snipey ult (and Corki's for that). It's just that new passives seem to more accurately and singly define a champion, and those two in particular suffer from very anachronistic passives. One basically has to walk right into Kog's passive and I'm not sure I've ever heard of Corki's split damage being mentioned in his stylings or his balance.
Ofc like I said I ain't really a Corki guy (or a Kog guy at that) but I heard the ideas and thought they were neat.