You are right. I have always been conscious that my dog might give me away. She wears a distinctive red harness which is another give away. I have thought about getting a different one.
On the plus side she is a Cockapoo of a common colour, and they are one of the most popular dogs around here – I see loads every time I go out. and she does give me a valid reason for being out here in the morning. Hiding in plain sight.
I have noticed that cyclists and joggers are usually so intent on their exercise that they don’t pay me any attention at all.