It should be possible - while phased out in new equipment, NiCd cells still are available for repair purposes. Still, the F3 is 30 years old, and its quick charger will be way out of spec for dealing with current NiCd cells, so any replacement might be rather short-lived.
If you intend to work that drive seriously (rather than charge it once and dump it on a shelf), I suspect that getting another MD-4 with battery crate (these seem to be much cheaper than separate battery crates), a set of NiMH cells and a charger for the latter might be a much better and cheaper long-term solution...