Did it really take me 22 years to find this out, or is it something I once knew and then forgot, to know again

Or puppeteers could only have two hands...

But the lab accident fits the character better.

Yeah, storyline wise it would make sense that Beaker lost an arm in the machine somewhere, but yes he usually has two hands.
The Beaker Army only has one because... well, there have to be at least 9 people all crammed under that set to get Bunsen Honeydew(mouth and two working hands so 2 puppeteers at least), and all the Beakers on screen at once, if you added an additional guy for arm perfection that's up to what at least 17 people? That's probably breaking the laws of physics, even for Muppet Labs.
Damn, I just spent too much time thinking about the logic behind Muppet Show bits.