OK, I've had a play with six different mics.
Shure SM58 I already know sounds OK.
Next was a Realistic Highball, which is a SM58 clone, sold by Tandy (Radio Shack). That was slightly quieter than the SM58 but no problems.
Next was an old black mic with no branding on it, but looks similar to an SM58. This was the loudest so far, but still can be used without causing any uncontrollable distortion.
Next was an AKG C1000S condenser mic. This runs off a 9v battery when there's no phantom power. More sensitive than the dynamics of course, but still no cause for concern.
Next was another condenser, but a cheap one sold by Tandy in the 80s, with a hardwired jack plug. Again, works fine.
Finally I tried a cheap radio mic (Gemini). I can get the VMS4 input to distort like crazy if I turn up the output volume of the receiver, but at a sensible level it works fine.
I'm not going to bother testing with any more mics because it seems to me that as long as you're not shouting into it while it's half way down your throat, or using a radio mic with the output set too high, it all works fine.