Yes. Exactly what Son of Mortarian said. That's what I should have said, if I was being helpful instead of a doofus.
As pretty much everyone has suggested so far, in fact, the best way to go seems to be an elite daemon-infested force that has the same stats as GK, but a different justification.
It does get very very complex if you want allies though. Chaos marine allies have to be loyalist marines that 'count as chaos'... but you can take inducted 'traitor' guard, I guess... and crucially, your models must be clear if you're using the 'counts as' principle.
For instance, I use the Blood Angel Codex for my Chaos marines force. But my Chaos marines are red, except for my "Death Eaters" (Death Company World Eaters) who are painted black. My 'regular' berzerkers have bone helmets (like the BA yellow helmets) etc. So apart from the models being chaosy, the paintwork 'looks' BA (and colour, eg of helmets, is the main difference between BA units), so there should be no surprises for my opponent.
As long as you bear in mind the principle that what you're representing should be obvious and/or logical (so things that look the same have the same rules), 'counts as' can be a really liberating way to play.
But, whether you decide to go down the 'somehow corrupted Grey Knights' route, or the 'elite Chaos force that just happens to use the Daemonhunter Army list' route, I'd be interested to hear what you come up with to explain these terrifying new servants of Chaos!
"Well it's Forty-one Thousand Nine Hundred Sixty-nine OK -
Gotta war across the Milky Way - "
Iggius Popiscus and the Stoogii, "41,969"