You are using a term that carries present connotations into the past, so that is the first problem here. The idea of "conversion" is something understood by today's Christians and followers of Islam to mean giving up one's faith in a spectrum of supernatural powers and adopting the religion described in the literature of one of those two religions (or giving up an absence of faith and arriving at a point of believing in something).

Pre-Christian Scandinavian belief systems were called a pagan religion by Christian writers, but they had few hallmarks that were comparable with the Church of Rome. A non-Scandinavian enslaved by Scandinavians before conversion to Christianity would and could make a series of personal choices as to what to believe and what to practice. The slave could continue practices he/she knew from childhood, and those practices would have been linked to a non-Scandinavian belief system that would have been informal and loosely applied at best (unless our slave was a Christian or a follower of Islam). Our slave might have found it reasonable or useful to adopt Scandinavian practices that seemed effective in eliciting the favor of local supernatural entities. He/she would have been warned not to do certain things that would clearly offend the supernatural, and unless our slave were incredibly sophisticated, he/she would have complied in "good faith," assuming that it was better to be safe than sorry when dealing with the supernatural.

In spite of all of this, the slave would not have gone through a "conversion" process in the manner implied by your question. There was nothing really to convert to. The slave may have adopted some local practices and come to believe in some of the locally-described supernatural beings, but that would be the extent of the transformation of his/her belief system. It was the informality of the non-Christian belief system and the practices associated with it, that made it so susceptible to conversion at the hands of a highly organized network of missionaries and priests. And they had a secret weapon: namely, their religion was written down, and that has always been hard to argue against.

Sources for this sort of conclusion are difficult because primary sources tend to be written by Christians a century or more after conversion. Both the Elder and the Prose Eddas provide an understanding of the Scandinavian belief system, but they portray a degree of organization that is probably unfair. I rely on the analogy of faith and belief as captured by the folklore collectors of the nineteenth and early twentieth century. When considering the folk faith in the supernatural (aside from that described by the church) we see a body of tradition that holds together loosely, but it is not organized, it is enforced only in the most modest of ways, and it can be surprisingly amorphous. I hope this helps.