Suppose we hedge an index option using futures on that index. How would the hedging strategy be different if the underlying could be traded directly (from a risk point of view)?
The differences essentially boil down to liquidity and pricing discrepancies between the underlying and the futures of the underlying.
With futures you have to consider basis risk which you obviously do not face if you can trade in the underlying directly.
Additionally, you need to roll futures contracts before they expire, hence you are faced with roll charges.
Also, depending on liquidity profiles, there are assets in the market where for specific reasons the derivative is more or less liquid than the underlying itself which may impact spreads and prices you pay/receive when trading them.
Another factor are financing charges: Some assets command higher or lower financing charges and borrow rates than their derivatives. Derivatives can most often be margined more cheaply than the cash underlying.
Those, in sum make up the differences and impact risk when considering whether or not to trade directly in the underlying or its derivative.