scai
The wiki description "which are not normally used as through routes" shouldn't be taken too strict. Local residents will use all kinds of roads as through routes since they will use any shortcut they can find. The question really is whether non-local people should use this road as through route. I can't answer this question, only local people can.

Either way, unclassified is wrong in my opinion. If you think that residential doesn't fit and if you convinced that his is a road with higher than typical traffic then choose tertiary instead.