Those are what I use if I’m not bolusing my whole dose via pod.
When I use pens, I use the Nano 4mm needles. Never had any leaking problem with them. 4mm is basically 3/16 inch, so I’d think they’d be safe for a child – and perhaps less painful or at least less terrifying than a bigger needle? @ClaudnDaye, if needle depth is the issue, why not use a pen with the shorter pen needle instead of a syringe?
Or prime up, but tap the pen against a finger before injecting, to flick off any stray insulin.