If he was illegitimate, this lessens the chances even further of there being a parish record of his birth/baptism. As well as this, even if it was to exist, the likelihood would be that he would be recorded under his mothers surname.

There may be a record of admonishment in the Kirk Session records, but you would need to know which parish it was in first of all, as there are no indexes.

Other than "Fraser" and "Invernessshire", what are the small details you refer to that make you think George is the son of Simon ?