Is the word "believe me" considered Shirk if said to avoid excessive swearing, and not for the purpose of glorification or making an oath?

There is no harm in a man saying to another, "Believe me," if he is truthful. This statement has no connection to shirk (polytheism). If he is lying, then he has fallen into the sin of lying, not shirk. And if lying when swearing by Allah is a sin, not shirk, then lying in the statement "Believe me" is even more certainly not shirk.