Calculating the energy of the $100$ nm photon, we get $$\frac{hc}{\lambda}=12.4 ~\mathrm{eV}.$$
This energy is well below the typical proton separation energies of nuclei, around 8 MeV (roughly a factor of $10^6$ larger). This means the wavelength of the photon would be on the order of 100 fm! But, there are photons of that wavelength (and energy). They typically arise from cosmic or man-made processes, and we give them the informal name of "gamma rays." Technically, a gamma ray is a photon emitted by a nucleus, but many classify any photon of energy about about 200 keV as a gamma ray.
These high-energy photons with $E > 8~ \mathrm{MeV}$ can certainly knock a proton out of a nucleus, but it must have a direct interaction with the nucleus, disturbing the nuclear potential.
Typically, the term "ionizing" is reserved for the addition or removal of electrons from an atom. One rarely speaks of nuclei as being ionized because the nucleus has a positive charge. If we change the number of protons, we actually change the element. You can't talk about removing a proton from nitrogen and getting ionized nitrogen; it's carbon.
Neutron and proton separation energies and probabilities are dependent on the particular N,Z nuclide, but whether the nuclide is stable or radioactive doesn't seem to enhance particle separation as a general rule.
Because the atomic electrons are so far away from the nucleus, they have little-to-no effect on particle separation energies.