<home airport> - NRT - HKG (until DL cancels the NRT-HKG flight; it recently axed NRT-PEK, and last year axed NRT-ICN and NRT-PUS both)
If you can book KE (on a DL 006 ticket you can, either KE or DL coded if DL codeshare is available), then <home airport>-ICN-HKG is the far better choice: better aircraft, better service, superior connecting airport, better lounge at ICN, and much better arrival time (not late at night) and departure time from HKG (with KE you can depart HKG in mid-late afternoon, vs. having to do so in the early morning with DL and then waste the whole day at NRT given DL's love affair with the many hour long connections at NRT).
There are many more options on SkyTeam (CI via TPE, CZ via CAN, MU via PVG) that you can ticket as a 006 ticket by calling (not online), but if it has to be DL coded flights, then you have less options. It's pretty much DL via NRT, DL coded KE via ICN (if available), or DL via SEA (service begins June 18)*.
*As of June 18, 2014 you also have an option of:
<home airport>-SEA-HKG on DL
**Expect to get the NRT-HKG flight axed later this year, given how DL is reducing its capacity and has recently cut NRT to PEK, ICN, PUS, ICN to ROR, and so on.
TIP: easy way to search:
1. Go to
www.kayak.com
2. Search for your flights.
3. Sort by the shortest flying time.
4. If needed, select Delta or SkyTeam only flights (for the latter, may need to deselect the Multiple Airlines that still remain selected).
You will see the shorter to longer flying time options and the rates. Often you can find better flights on kayak.com and then go to delta.com to book it, than delta.com will give you itself.
I suggest you clarify your corporate policy. Does it need to be:
(a) Delta
operated flights?
-or-
(b) DL
coded flights? (i.e., doesn't matter who operates it as long as it's coded as DL xxxx)
-or-
(c) Simply 006 (Delta)
ticketed flights?
(a) is the most restrictive and silly, with (b) you have a bit more choices, while with (c) you have a whole plethora of SkyTeam options (DL, KE, MU, CZ, CI, and VN), just will need to first piece it together, then call DL to price it out and ticket.