It is almost impossible to trace an unnamed father of an illegitimate child. A child can be registered under either mother or father's name and it is not necessary to identify the father. If it was before 1855, then there would be a good chance the couple would be brought before the kirk session to answer to their sins but when compulsory registration of events started, the churches did not pursue the practice for long. Perhaps close friends or family knew at the time but unless the information was passed on then there isn't much can be done. I have tried on one or two occasions and the only success was the report in the kirk session records. The last remaining member of another family died a couple of years ago, taking her secret with her - as did her brothers and sisters, nothing could have persuaded her to tell - we did try! My friend's mother was born in a hotel but we think it was a case of keeping things quiet, we don't think her g/mo worked in the hotel unless just to pay for her keep until the child was born. Parents often sent pregnant girls away from home who were then often forced into having their baby adopted as they had no means of supporting them. They would also find it difficult to get work.
You could be lucky if someone has passed the information on, do you know any family or friends who would have known and passed the information on to their families. Answers quite often come from the least likely places, so good luck with your search.