If the cable itself need no mechanical protection then I would avoid the weight of the SWA. Don't aim for too tight a wire as it massively increases the forces to get it there, and reduces the tolerance to changes in tension with temperature, wind, ice loading in winter, etc.
That means you will get a bit of movement in the wind, and so the suggestion above for rubber HO7RNF is probably best as it is fine-stranded and going to last longer with some flexing, as well as being outdoor/UV rated. Also allow a little loop where it goes from wall-fixed to the wire so no tight flex radius at that point.
Finally remember to put ferrules on the ends though so it is reliably terminated!