I usually disband the cigar, then take off the wrapper...then unbind the binder and filler. It take a sec or two but its interesting to see and sometimes you'll see two different binder colors.
And then whip out the Lava soap to get the stank off your hands! :ss
I've actually often thought of disecting my cigar but haven't yet. I probably will do it because, like you, I'd like to see the innards and I'm not going to ruin any cigar beforehand out of curiosity, no matter what it is!
Once I'm done, I cry a little and ask my wife to hold me....and then pass another stick my way.
But seriously, I let the cigar go out, take the band off if it's still stuck on there and I was too worried about fiddling with it too much while it was burning. I put the band in my pocket or wallet to put in my journal later (where I keep a log of the type of cigar, size, when & where I bought it, the rating, price, where I was when I smoked it, what I thought about it, etc. - so i can come back & see what I liked when my humidor is low).
Then I'll throw the nub in my sand pail where I collect a few until I get off my lazy a$$ and throw a bunch of them in a ziploc bag and then in the garbage can. The ziploc bag keeps the smell inside and all the stray ash & bits and stuff.