I believe that if you chop it fast enough, the persistence
of vision (and phosphor "hang time", on a white LED)
will let you go without an inductor. You might be able
to get away with a simple emitter ballasted NPN switch
or something simple as that, driven by a logic gate, on
the low side and varying the pulse width of that fixed-
"on"-current train could get it done. Emitter resistor
sets the current as (VlogicH-Vbe)/Re. If you have some
other thing that would source a variable logic pulse width,
this might be your lowest incremental cost approach.