As far as I know, nothing. At least nothing practical. Even if you manage to get the glumps of it out, you're probably not going to be able to get ALL of it, and that little bit is still pretty bad.
I've never tried to get vaseline out of a cube (never put vaseline INTO a cube), but I have grabbed a handful of vaseline before and worked it inbetween my hands, took forever to get it off, and it never really went away, at least not for a few days. If you're really hell bent on getting it out, I'd say first wipe it top to bottom, inside and out (cant do that with a storebought), qtips, kleenex, the works. Then use a wirebrush on the rest, changing the brush every 2-3 pieces (or more), and cleaning your hands (washing doesn't work) with a towel between each piece.
...but I don't think it's worth it. Sorry.