
Does he wear th harness when eh is of the lead? If so then I think you will be fine.
My dogs wear collars and tags 24/7. There are dangers in both wearing and not wearing one.
In my case I feel there is more danger or likelihood of danger not wearing one, as I live on a busy road ,and a moments inattention from visitors and a dog could be out of the house (small hall which means people are often through to living room before front door is closed.
My dogs do not easily panic, and even when playing have never had one get caught up in another's collar, but having thick coats with the collars nestled in their ruffs helps.