A method is proposed to determine the Formula Presented nuclear transition amplitude and hence the lifetime of the “nuclear clock transition” between the low-lying (Formula Presented) first isomeric state and the ground state of Formula Presented from a measurement of the ground-state Formula Presented factor of few-electron Formula Presented ions. As a tool, the effect of nuclear hyperfine mixing in highly charged Formula Presented ions such as Formula Presented or Formula Presented is used. The ground-state-only Formula Presented-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like Formula Presented ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.