inner fragments? like from the tube? nah, these will go along just fine, or maybe the tube is plastic anyway

your line of thinking is mostly correct, look up wiki article of claymore mine, section development for more detsils - you need uniform layer of soft steel, gaps filled with something, optionally with a thin sheet of liner that will contain gases just a little bit longer, and it can’t be too heavy compared to filler so these fragments can develop reasonable velocity, and these fragments can be probably much smaller than you think. a little math goes a long way here