Immersion blender substitute? Could I dice and mix with whisk?

Not at all. the blender has cutting blades that puree the soup. a food processor will do that too but not as pureed (smooth) as a blender. Immersion blenders or blenders- both have blades that puree . BTW, a whisk just stirs something, basically; it doesn't cut anything.

You could also use a potato masher or a ricer if you don't have a processor. you just have to make sure all your vegetables have been cooked til they are very very soft and easy to mash thoroughly without lumps.