The Golden Age Wesley Dodds was reasonably athletic. We see him running, jumping over hedges and vaulting into his roadster, punching out two thugs at a time... kind of the standard mystery man level. This was from the start, when he still wore the gas mask.
The Wesley Dodds from SANDMAN MYSTERY THEATRE was an average specimen, a bit out of shape. He relied on the gas gun to avoid brawls, and was more a detective like Ellery Queen rather than Mike Hammer. I guess the current history is that this Wesley was motivated to start hitting the gym big time because he was motivated by seeing what the other mystery men were like. The trend was toward colorful costumes and he got one for much the same reason men get new haircuts, to not be too out of style.
I like both versions, and don't feel I have to choose between them. But then I'm not that big on seamless official continuity.