mortice chisels are relatively inexpensive, and I haven't yet found the gospel that says you cannot hit them with a hammer. Of course they will never fit into a mortice chiselholder
BUT the tiny points will splay as it's hammered in, so a few taps and you have to stone them flush again
Too many taps, the splayed points are gonna lock the mortice bit into the wood.
In my mind, and from past experience, a hand drill is difficult to use enough force to push the mortice chisel into the wood,