in your case the main problem is that the absorbency of the bare patches will be greater than the painted ones, so the texture of the paint will look different. Apply a couple of coats of emulsion thinned with 20% water, it will quickly soak in and dry, then a couple of coats unthinned so the surface has a layer of paint on it. Then, when you paint the whole wall, it will have equal absorbency and the texture and reflection of the finish will not look patchy.
It's more economical to use matt white if you need to buy extra paint for this patching, but if it's just a small amount, the paint you already have will do. You only need to take the shine of your existing silk where the new paint will overlap onto it, a 600 grade wet and dry paper (as used for painting cars) is suitable and you need very little. Any coarse paper will leave visible scratches that will show throw when the light falls across it.
Clean the surface and remove all traces of dirt, grease and wallpaper paste before painting.