As a non-english person and as a runner, I would prefer talking in favor of conversation. Conversation can come after running, but I can't imagine it during the running. But still, English is not my native language... Maybe I only project my view from my native language into English.
Even in UK English, you won't find many people using it as part of their day-to-day vocabulary. People will mostly use when instead of while.
I would say so, since I cannot think of an equivalent for "chat." «conversar» is not as formal as "to converse" in English is. That happens frequently; for example, in Portuguese, we often use «contente» as a synonym for «feliz» or "happy," whereas in English "content" sounds more formal and implies more of something along the lines of "satisfied."