Load test would be pretty straight forward as long as you have something to anchor a tension line to in the vicinity of the handrail. You could contact a local company to does fall arrest testing, or maybe a company that provides and installs rigging could help.
You could also test it yourself fairly easily. Get your self a load cell appropriate for the applied load (probably 50-200lbs range, check local codes)and a means of applying tension. The load isn't too high, a small diameter cable and turnbuckle would probably work. Check the posts for any distress and for plumb before the test, apply the load to the post and hold for a few minutes, then check again for distress and make sure the post returns to its original position. Repeat similar procedure for the rails.