IMHO body resonances don't necessarilly affect the sound of the recorded mic at all, depending on whether the resonance is audible to the diaphram of the mic.
MANY cheap mics have bad body resonances, even some expensive mics. only one I know of to this day that is audible in any obvious way is
the apex 210 I owned for 1 day (same as the rest of the big bodied cheap chinese ribbon mics, as opposed to the small bodies cheap chinese ribbon mics which are better built). That mic had a resonance IN THE GRILL, or at least connected to the grill somehow, and touching it made a ring that was not only audible in the room but audible in the element of the mic. I traded it for a 205 and am much happier, not that it's a great mic by any stretch, but it's at least useful for my intended purpose of buying one.
But there are some amazing sounding recordings done with mics that have body resonances. As long as the diaphram is mounted in a suspension of some sort (rubber, foam, or something similarly non-resonant) you shouldn't hear anything come through the mic unless you tap the mic stand or something like that.
If you don't like the adk hamburg you probably won't like it with the resonance removed from the case either.
Famous cheap mic with body resonance that isn't audible in standard use: apex 460 tube mic. tap that baby, nasty resonance. mount it to a stand, listen to it, record with it, as long as you have a good sounding one (they vary WILDLY from personal experience) it'll sound really really good, no hint of the body resonance coming through. It's actually a well built mic.
Now, if I were building a mic to sell, I'd make sure it had no obvious resonances in it, because for one thing it is a more satisfying feeling to pick up a mic and have it feel solid and not ring when you put it down or tap it. But as long as the designers did their job ok, you shouldn't have any problems in standard use, from my personal experience. It's not like loudspeaker resonances where the tone is behind the diaphram affecting it's load in the box. a mic body resonance doesn't touch the sound waves being recorded at all (at least in cardoid, figure 8, etc) and the only way the sound could be picked up is through direct or sympathetic vibrations into the capsule from the body. That definitely can happen, but it, um, well, it shouldn't I guess is a fair way of putting it, and from my own experiences with tons of cheap mics (even radio shack and other cheapos), I've never found it to affect the recording with only one exception, the apex 210, a nice looking but shockingly poorly damped mic.
So definitely damped it if you want to, it might improve things at least slightly in how you can use the mic, but it really shouldn't change the sound of the mic itself. If you don't like it now, I expect you'll be doing all that work for nothing and you won't like the mic in the end either.
Best of luck either way to you (if this is still valid to you) and to others hoping to change a mic's sound through that technique of dampening body resonances. Just get a different mic and be happy.
Don
