You can override Block#getPlayerRelativeBlockHardness(IBlockState state, EntityPlayer player, World worldIn, BlockPos pos), check if the item in player's main hand is shears and return a lower value.
Dragons stay alive after death to show their death beaming thing. You can see this by shooting them with projectiles very fast when they are "dead", they will still get knocked back, and if knocked back far enough will start moving around again. They also start rotating in apparently random directions when hit at this stage.
Hope this helps