The phosphor bronze wire offered by Tichy Train Group is a very common choice among modelers for forming things like handrails and air piping. They have a half dozen or so diameters to choose from, and a couple of lengths.
Two other choices would be brass rod and piano wire. I believe the brass rod won't be as resilient as the phosphor bronze, for the types of diameters needed. Piano wire is certainly strong enough, but is hardened, so will potentially require different tools and techniques for cutting and forming. Neither, as sourced from K&S Metals for example, comes in diameters as small as for the phosphor bronze. However, they are both offered in .020" and up, so they could work for O scale handrails.
Jim
Edit: John mentions the hardened cutters for the piano wire. You can also cut it with a Dremel tool with a cut-off disc. This also has the advantage of leaving a "square" end to the cut wire, as opposed to a pinched end from diagonal cutters. However, a few swipes with a file will dress the ends.