Is it considered a mistake or a sin for a speaker to pause their enjoinment of good or forbidding of evil when girls or young men pass by, due to shyness, and then resume the conversation after they have moved away?

It is not true that shyness from performing worship in front of people is better; rather, one should not be shy from worship. What the questioner experiences is likely from the whispers of Satan. There does not appear to be any justification for prohibiting the cessation of offering advice to someone until passersby have gone, due to shyness.