I'd choose either a galvanised wire or aluminium (preferably round, not square-section). At a gauge I could manage with the strength and tools I have. If I needed it thicker, I could double it/twist it together.

I'd pass on anything with a plastic coating because it doesn't always last too long in exterior conditions.

My first thought was to use the boxwood shrub alone by trimming, without wire. How big do you want the swan shape to be? And how long are you willing to wait for the neck and tail, because it will take patience but it can be done. Depending upon how big your swan is to be, you could buy one shrub or plant two shrubs close together. Or buy a really big boxwood shrub and trim it up (or should I say "down"). I'm sure you can achieve an arched neck eventually, then at that point you may need to use wire to coax the leaves and stems to make the arch. Were you going to create wings, also?