Not the grau man, it's the ultimate bumchum weapon these days, you hardly see anything else.
I'd recommend the ram7 to go with the hdr. In my opinion it's the best ar to cover close-medium ranges, probably the only ar that I'd be happy taking on a decent smg with at close range.
Ram/Hdr and Mp7/M13 are my two favourite loadouts.
If you're using your AR to cover mid-range while also carrying an HDR, you're Warzoning wrong. Unless what you consider mid-range is WAY shorter than actual mid-range, you should always be HDRing. The idea that you would rather use 8-14 AR bulllets to down someone rather than 1 headshot from an HDR is ludicrous. The only situation where you'd prefer your secondary is CQC when using a single-shot sniper for headshots isn't feasible.
OP - use an SMG. I prefer the MP5 but the MP7 is a good choice too as Aurrican says. Kit it out with attachments that improve ADS time and sprint-to-fire speed - being able to fire before your enemy in CQC is huge, even if it's just a 1 bullet advantage. You don't need to worry about controlling recoil as much because in CQC targets are huge because they're literally right in front of you. For the same reason, aiming stability doesn't matter because aiming stability is a thing you deal with when you're ADSing medium-to-long-range targets, which you will be using your HDR for. It's still good to keep a suppressor on there, because anything that avoids drawing attention from surrounding players is a good thing.
I have my MP5 kitted out as follows:
Muzzle: I prefer the Lightweight over the Monolithic here because the latter costs you ADS time, and the only added benefit is damage range. We don't care about added range with a CQC because most of the time you're using this weapon it will be from 20m in. Both suppressors do the same job in suppressing sound from what I've seen/read, so the faster ADS time makes the Lightweight a better choice here.
Barrel: The goal here is for faster ADS, and the FSS Mini also offers a + to movement speed. Faster movement speed gives you so many advantages, from getting around the map faster to being able to reposition/flank enemies quicker. Lower bullet velocity doesn't matter because that only affects bullet drop and at CQC that is irrelevant. The Mini does hurt recoil a bit, but at CQC recoil is less of a factor than midrange and the added movement speed is worth it.
Laser: Debatable to use one, but if you do the Tac is the only one worth using for it's ADS speed bonus. However I prefer a Mag attachment for my 5th slot.
Optic: I skip an optic altogether - not necessary for CQC and it allows you to swap for another attachement.
Stock: The FTAC is the easy choice here. Bonuses to movement speed and ADS speed - nothing else comes close.
Underbarrel: Skip altogether. These all try to give you some kind of recoil or aiming stability. Recoil isn't an issue short range, and each of these costs you in either movement speed or ADS time, which is a no-no here.
Magazine: The alternate choice to a laser. The extended 45 round mag is a no-no because it slows both ADS AND movement speed. The 10mm mag adds some damage and range at the cost of fire-rate, so in essence it makes it more of a mesh between an AR and an SMG, which is perfect if you are using this with a sniper. It extends the useful range out to 30m instead of just 20m.
Rear Grip: Stippled Grip Tape adds a plus to ADS speed and sprint-to-fire speed is exactly what we're looking for with this weapon so this is an easy choice. Aiming stability is more important for medium/long-range/sniping and isn't a factor for CQC so the tradeoff is minimal.
Perk: The only choice that would make sense here is Sleight of Hand. However I really can't justify removing any of the other 5 in my personal opinion since ADS speed, movement speed, and sprint-to-fire speed is what this weapon is all about. If you've sprinted yourself into a squad you have more problems than needing a reload that is .5s faster. Use better game sense and you should be fine without it.