This narrative is seemingly useful for dawah and would hardly be questioned by premodern Islamic historians. Also, do we have surviving non-Islamic Arabian sources to present their perspective?
Yes, there are historians that have started to work on Islamic history from the perspective of Late Antique sources, and are more critical of early Islamic chronicles. The revisionist school of Islamic studies began in earnest with School of Oriental and African Studies in London during the 1970s, and one of the main studies to come out of this was a book called Hagarism by Patricia Crone and Michael Cook. This book was extremely controversial when it came out and the argument has since been challenged and overturned, but it is still very important in that it introduced a more critical approach to early Islamic sources.
A more recent book along similar lines by Robert Hoyland called In God's Path reframes the early Islamic caliphate by arguing that while Muhammed and his followers did conquer and expand, his group was one of many Arab groups expanding into the Levant and Mesopotamia in late antiquity. He works primarily from Late Antique sources written in the region, and his previous work was a collection of non-Islamic sources on early Arab conquests.
As far as the Arab pagans in Mecca, the Quarysh clan distrusted, and were later threatened by, Muhammed because he would have upset their control over the Kaaba and the then-pagan pilgrim routes to the city. I am personally unaware of sources written by them, as most of our information on them comes from either the Koran or Arabic chronicles written about two centuries after the death of Muhammed.
While a bit later than the time period of your question, you can also find the writings of Saint John of Damascus or Saint Thomas Aquinas' Summa Contra Gentiles that lays out medieval Christian views on Islam. They generally viewed it as a heretical sect that combined Christian doctrine with syncretic elements. Of course, with these Christian writers (excepting John of Damascus) access to Arabic was limited as was availability of Muslim texts.
Hope this was helpful