In this work sharp silver nanotips are analyzed and proposed as useful plasmonic tools to reduce the threshold for the onset of strong coupling in the electromagnetic interaction of a point-like emitter with localized surface plasmons. If compared to similarly-sized spherical nanoparticles, conically-shaped nanoparticles turn out to be extremely useful to reduce the oscillator strength requirements for the emitting dipole, a reduction of the threshold by one sixth being obtained in a double cone configuration. Moreover the transition to the strong coupling regime is analyzed for several cone apertures, revealing a nonmonotonic behavior with the appearance of an optimal cone geometry. The emitted-light spectrum is obtained from the computation of the perturbative decay rate and photonic Lamb shift in the classical framework of the Discrete Dipole Approximation. This combined classical-quantum electrodynamics treatment is useful for the theoretical investigation on nonperturbative light-matter interactions involving complex shaped nanoparticles or aggregates.