Something else not yet mentioned...the combination of white skirt tetras with angelfish. This tetra is the same species as the original black skirt, and they are known to enjoy harassing sedate fish like angelfish. All cichlids are sedate, so before any dwarf cichlid is decided, I would suggest removing the white skirts. Past trouble with fin nipping may not have been physically evident, but introducing a new fish into this tank might set it off. Plus there is the chemical signals, allomones, all fish release that are read by other species (pheromones are chemical signals read by fish in that species) and fish can suffer stress from these, unseen by us (assuming no physical follow-through by the tetras) until the fish "dies."
Turning just to the question of a group of cories, yes, this will work but we do need to pin down the source water parameters (GH especially, pH worth knowing too) and temperature is the other parameter that needs to be considered depending upon what fish you consider...the cories do not like heat, so 75-76-77F (25-26C) is as high as it should be long-term for cories, and most shoaling species will appreciate this too...but some cichlids will not.
Turning just to the question of a group of cories, yes, this will work but we do need to pin down the source water parameters (GH especially, pH worth knowing too) and temperature is the other parameter that needs to be considered depending upon what fish you consider...the cories do not like heat, so 75-76-77F (25-26C) is as high as it should be long-term for cories, and most shoaling species will appreciate this too...but some cichlids will not.