When I approached them concerning one of my father's medals they didn't require a death certificate. They did need the details of his service, eg his regimental number, DoB, etc, and then they went into the records themselves even though I had sent them official copies which the Records Office had sent me! It took a while but was worth it in the end.
With the OP's relative's unfortunate situation of being killed during training, perhaps there could perhaps be other hoops to jump through I suppose.