Is there a way to use the mouse wheel as a normal button, instead of an axis?

Not sure, but you can use the axis the way you want to.

 int SW = Input.GetAxisRaw("Mouse ScrollWheel");
 
 if(SW == 1){
 // You're scrolling up
 }
 else if(SW == -1){
 // You're scrolling down
 }

This is the same as a

 if(Input.GetKey(...))

But since there's not really a 'press down' and a 'press up' on the scroll wheel axis, if you want to swith weapon for example and you want it to switch only on the next or on the previous weapon on your list, you should add a SW = 0; on the end of both conditions, but not sure if this'd work.