Aesthetics has absolutely *nothing* to do with a choice such as this. Either it is a beneficial feature, or it is irrelevant. Any of the various J frames would work well in a CCW role, whether a Chief's Special, Centennial or Bodyguard.
Nothing wrong with a Mdl 36/37 as a CCW, just have to remember the hammer's tendency to snag on the draw, and cover it with your thumb as you draw. I would personally recommend a "Centennial" type Smith- either a 40/42, or some variation of the newer X42 Airweight models- they can be had without a lock, if that is of importance to you. For the *intended purpose* of this firearm, single action is absolutely unnecessary.
I would carry a reload on a speed strip, just on principle. Regarding carry.... the old 125grn +P JHP is still as good a round as ever it was, though I'd stick to standard pressure loads in an Airweight, simply due to recoil management. Failing that, a 148grn wadcutter is a better defensive bullet than RNL, while still being manageable in firing. From examining and testing buddies set-ups, I've determined *for me* that pocket carry will never work, not in jeans or slacks.
Also, another helpful (to me) benefit of a Centennial is that one can get a higher grasp on the backstrap, bringing the bore axis slightly lower.
To add to this in an edit, a single action may be beneficial on extraordinarily rare occasion. I personally have always held the belief that if you have time to use the sights, you have time to cock the hammer.