Using density functional theory (DFT), we study how the stability of individual magnetic skyrmions in an ultrathin transition-metal film can be controlled via the external electric fields. For applied electric fields of $mathcal{E}$= $pm 0.5$ V/{AA}, we find changes from 8 to 30$%$ of the Heisenberg exchange, the Dzyaloshinskii-Moriya interaction, the magnetocrystalline anisotropy energy, and the higher-order exchange interactions. Based on atomistic spin simulations using the DFT parameters, we find that the energy barriers for electric field assisted skyrmion writing and deleting can vary by up to a factor of three more than the variations of the interactions. This unexpected result originates from the electric field induced shifts of the critical magnetic field, marking the onset of the field-polarized phase, which exhibits metastable skyrmions. The shift leads to an electric field dependent change of the skyrmion radius at a fixed magnetic field and explains the enhanced energy barrier variations.
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