Have you ever tried carving a spoon with JUST a whittling knife?
If you have then you know it practically takes a lifetime to accomplish. Granted, it CAN be done, but if you want the bowl of a spoon to have a smooth finish then I suggest getting the best spoon carving knife (a.k.a. “hook knife”) to do it.
Luckily, for a decent hook knife, it is quite affordable to purchase and even easier to maintain, but I would not advise buying just any hook knife. You have to know which one is the best spoon carving knife before you can make a decision like that.