Sniffing

CM rehabilitates dogs. Sounds like that Beagle is a normal healthy doggy, with a lot of Beagle-energy pumping through: "Smells... smells!" But you'd be a better judge of that.

I think you're right on here.  I should have thought of this before.  Sometimes we get dogs that are just....good dogs!  They don't need a lot of correction (verbal or physical) and they aren't going to try to take advantage of you if you give them more freedom because they're already well-trained, well-socialized, and respect their handlers as the leader.  I suppose these cases are so rare and refreshing that I'm too quick to assume every dog is going to be totally erratic!  It makes sense I have a harder time realistically applying CMs methods in these cases because these (rare) dogs don't really need that type of rehabilitation.

Coming in to the thread a bit late here, but....
I suppose the bottom line is that someone who works with shelter dogs in the way that you do needs to make an educated decision on how to handle The Walk.  If there's a trainer, as in your case, see what input s/he can offer about the dilemma.  First, find out the training methods used. If s/he isn't an adherant to CM principles, then the ball's totally yours to run with (little metaphor here [] ).
Or, If the trainer thinks it's fine to let the dog determine the tone of the walk (or not), then perhaps you might want to base your decision on that. 
I know that my boy Dundee wasn't particularly open to other training until I managed to train him to keep his nose off the ground.  (We hadn't even heard of CM at that point.) Once we got that downpat, everything else suddenly started to fall into place.  But, obviously, the methods- and goals- need to be adjusted when you only spend an occasional short time with the dog, and when it may not be under your care for long.
And I agree with a past post (back on p.1?) that it's high time for CM to do a show for shelter workers.  (A whole show.) Fosters, maybe not so much, as they sometimes end up keeping the animals for extensive periods.