Resonant plasmonic helices have been widely utilized for locally enhancing and tailoring optical chirality. Here we investigate their nonresonant operation through the recently introduced concept of a plasmonic helical "traveling-wave" nanoantenna. Relying on the coupling of a nonresonant plasmonic helix and a nano-aperture, the helical traveling-wave nanoantenna transmits circularly polarized light with the same handedness as the helix and blocks the other, with a measured dissymmetry factor larger than 1.92 (maximum value of 2). This chiroptical transmission is spatially localized, spectrally broadband, and background-free. Finally, we demonstrate the possibility to engineer such a plasmonic helical nanoantenna at the apex of a sharp tip typically used in scanning near-field microscopies, thus opening the route for moveable, broadband, and background-free chiroptical probes.