the green on the asang is verdigris, very poisonous. on a small area like that you could use an old toothbrush (throw away/destroy afterwards) and a paste of baking soda & water to scrub it off, then rinse with warm water, dry lubricate. wash your hands well before eating.
i use ballistol myself. be careful of course not to get any (water/paste/ballistol) on the grips. ballistol tends to darken brass, giving it a nice patina. ballistol is mostly mineral oil with a few additives. some people do not like the anise/licorice smell. it was developed as a general purpose weapons cleaning and preserving fluid in the late 19c by the germans. it's even used medicinally as an antiseptic wound treatment. good for steel, or wood, tho it may darken it. same for leather. not recommended for cloth. it's a food grade edible product that can be used on food preparation equipment. not sure how it would fare on a complex kris hilt.
the steel should have any active (reddish or crumbly) rust mechanically removed as mentioned above. inspection is best done in sunlight to see the differences in the types/colours of the rust, red rust can look black indoors. the black patination in some areas should be left alone (but oiled).
brass brushes or brass wool, dental picks, pointy screwdriver, etc to break up any of the crusty red rust. olive oil makes a dandy lube for that. when you have absolutely all that will come off mechanically, you can stop, clean with hot soapy water, rinse with hot water, dry & lube with ballistol or mineral oil.
rust can also be stabilised after removing the loose stuff with tannic acid solutions. it's a safe product that will however turn the red cancerous form of rust into a stable black form, much admired and used on gun barrels. after treatment, neutralizing, rinsing, drying, you lube generously with ballistol & you are good for a fairly long time. p.s. - tea doesn't have enough tannins, it is used in beer and wine making and is available from some pharmacys or online. it's a powder you can mix in water. wear rubber gloves or be careful, it not poisonous but may discolour YOU...
in everything, take your time, be careful, do not expect a 5 minute effort to cure the problems.
google 'sword conservation' for more info, some is contradictory.
as may be some info here.