Recess them under the handrail and dow them into place. As for the balister-base, you can set them between 'tongues' (or spacers).
If you don't secure them in some way, they'll move on you. That would be quite annoying. They had nails 200 years ago. Is there more you can say as to why you're interested in a non-nail, non-screw installation? If it's just for the sake of not using nails and screws, it isn't worth it.