By the way, shapes are often used in physics engines to compute mass and inertia tensor....so unless you happen to have specific mass/inertia properties that you want to assign explicitly, you may need to leverage a shape anyway to setup your non-colliding dynamic object!
On to the question at hand.
I'm not familiar with the current Havok API, but there may in fact be a custom shape that is intended to create objects that won't collide. You might be able to, for example, create a sphere with a radius of zero, and Havok might have logic to consider that zero radius sphere as being a "no collide" shape. Although that is hacky. If this is the way it is, hopefully the documentation will tell you. More likely, in addition to a shape, the object can have a flag that says "NO_COLLIDE_FOR_THIS_OBJECT" or something like that....so the shape can be there (and may be useful for debug visualization...who knows), but isn't actually used for collision detection.
Some more thoughts... Many physics engines support the concept of collision groups. Collision groups enable you to explicitly set up objects that may interact over part of the game level. You may have 10 objects over here that can interact, and another 9 over there, but the 10 can never inteact with the 9. It is cheaper to treat them as two separate groups. The idea is that collisions are detected between objects within a common collision group, but not between objects in different collision groups. So, you could created a dedicated collision group for your object that you don't want to collide with anything. If you want to have many objects like this, it may be impractical to have a separate collision group for each. You could in that case add some custom user data to the objects and write a collision callback function that would ignore any detected collision between objects that you do not wish to allow to collide. That approach would still incur the cost of doing some collision detection...it would only avoid the collision response, effectively ignoring the collision. The cost could be mitigated somewhat if Havok allows separate callbacks for broad phase collision detection, which is the first and cheapest phase...basically do the bare minimal collision detection before it gets to the expensive narrow phase and collision response parts.