Cm4s are a little big for a hat but people do it
Schoeps, dpa, Neumann, akg, and geffel all have active cable solutions that work well in those spaces.
I own:
Line Audio:- A matched pair of CM4,
- 2 matched pairs of OM1/Omni1
Schoeps:A matched pair of CMC1L / MK21
A matched pair of CMC1 / MK5 (brand new so haven't A/B'ed)
A few matched pairs of DPA CORE 4060
Everything I do is recorded into a MixPre-6. I have also tried them into Sound Devices transformer pre's, which I like better (more beefy sound), but usually don't bother with added cables/setup/things to go wrong.
My Schoeps MK21 are more 3D and "sharp" than my line audio mics. The line audio mics are mellower. As spots on operatic voices, mellower can be a good thing, as the Schoeps MK21 can sound harsher. My friend, who is a top pro and much more experienced than I, explained that he felt the same, but MK22 were mellower than my MK21 and more like the CM4. On piano, I much prefer the MK21's sharp/3d'ness. By "much prefer", I mean that I can usually tell them apart, and there's a 1% advantage for schoeps (but that's just piano not voice, where CM4 may win the day), but still sometimes I can't tell them apart. On high-stress situations (135dB soprano off-axis), Schoeps does have a little advantage. I'm not deaf -- on Gearspace, there are threads with 30+ people absolutely certain that A is Schoeps and B is Line Audio or vice versa, and they're right 55% of the time... DPA is also a great sound. To me it's slightly more "granular". That probably is an ineffective word, but it's not really sharp in a harsh/beautiful way like schoeps, nor is it mellow like Line Audio. I wouldn't pick DPA for sound, but I do pick them for size.
MK5 cardio mode on spoken voice has the classic schoeps polish we know and love. Again, though, you're talking about spending thousands for something where sometimes you cannot tell the difference. Placement matters way, way, way more, as does the quality of your room.
If you're not a pro, and you don't just want Schoeps for personal satisfaction, then probably not worth the outlay. I love them both, but it's also just something that brings me joy. Also, I'm recording 135dB sopranos off-axis where any distortion is immediately noticeable to the human ear. No way you'd notice on a guitar or piano.
I have found that when I bring Schoeps and Sound Devices, other A/V pros are much more willing to take me seriously and lend me gear...so there's that.