Carb cleaners are usually "ether" which covers a multitude - some are more water soluble than others, for example.
I'm sure that Tygris would be great - may get some.
If yours isn't ferrous rust won't be an issue, which it often is.
Alcohol, usually propanol or IPA, (IPA but not the Ale) is pretty good with greases but not quite up to acetone, which is of course very dissolving of many things, and quick to dry. You need it 99%+, not nail varnish remover. Just don't order high % hydroen peroxide at the same time...!
Oils particularly ( which includes most greases) dissolve well in what the Americans tend to call "naphtha" which isn't very specific but hydrocarbons. Our goto equivalent is lighter fluid, which eg a locksmith will use to clear gunk out . It's good. Car petrol isn't bad, but has a million additives.
The ultimate dissolve-everything jizzm (it'll have a go at a kitchen laminate) is graffitti remover, it's vicious but damn, it works.
Remember with any of these, you have to remove the liquid
before it evaporates, otherwise you just distributed your grease nice and evenly.
So paint some on, soak it up in a lens tissue, and repeat.
For replacement grease you can use a light lithium grease, though there will be tight tolerances on the original - some optical greases cost several hundred dollars for a tiny bottle. Look at "Nye".
But never never never ever be tempted to use silicone grease on anything optical,. It waits until you aren't looking and spreads itself one molecule thick on all the surfaces, including the glass and it's impossible to remove.
If you do get any (normal) oil on glass, this stuff is the d's b's:
http://www.newprouk.co.uk/ROR-lens-cleaner.html
It would probably work well on your fracture surface, which will have many nooks and crannies. brittle fractures show a lot of grain boundaries, like mini broken expanded polystyrene. More ductile fractures have tears, and won't fit back together so well. May be too small to see.
Apart from things like camera sensors, I've used ROR on spectroscopic, laser and imaging equipment. £20k per lens, in some cases.
It is wet, you do have to remove it with a lens tissue (NOT a Kleenex), but it's awesome. Dry with IPA or acetone.
