Well they would not get to SKORR.
So it wouldn't be a RNAV departure.
Of course you can have departures only work for certain runways but that normally means a routing change as well.
At JFK all planes get vectored anyway no matter which departure they fly so it would be possible to have such a strange SID.
But you are right it wouldn't work like i suggested because all SKORR departures get a transition assigned that would no longer be valid.
So yes the change should go into the Kennedy 5 departure. Still much less talk to assign the Kennedy 5 instead of the Kennedy 5 with all the extra stuff that needs to be read back.
And i've heard early and no turn at all resulting in that "custom" SID.
Anyway they have something like it already:
https://de.flightaware.com/resources/airport/JFK/DP/DEEZZ+FIVE+(RNAV)/pdfThat's not really an RNAV SID in the strictest sense. It's some RNAV some vectors back to RNAV.
Anyway it does not matter how you implemented it but it would be useful to put the "100 heading after JFK 1.5 DME" on paper, and it's quite obvious it's not being put there for strange bureaucratic reasons, which is always sad to see.
And just to make it clear: The departure procedure does not have any conflicts because it is what everyone departing 04L at JFK get's as a clearance most of the time. It's not like they are issued these "vectors" after takeoff as an instruction, rather issued before as a clearance together with the route.
The clearance is designed to get out of La Guardia's way while protecting from conflicts with go-arounds on 04R.