We love this kind of stuff. You should be able to get a colour match pretty bang on, it just takes to years of practicing colour matching by eye, which my resident artist(repair lad) can do. Profile it down to the correct shape and polish the fill in line with the tile. There are some sneaky products you can use to polish the filler. It will cost you about £10 in total for products. No need for the Konig kit
I will post some pics of some heritage work with did with repairing ceramic wall tiles.