Best to just buy a suitable chuck, but I have seen soft pieces welded to chuck jaws such as you show, and yes, jaws are quite hard, can be drilled with carbide, but not tapped; another possibility is to anneal the jaws, then they could be drilled and tapped, for your application having them left soft would not matter so far as possible wear is concerned, and yes, leaving the chuck wrench in the chuck is the biggest NO-NO in shop work, it is just not done, if the machine is accidently started the wrench goes flying and what it hits, suffers.