Yes, a Tiny-sized Eldritch Cannon (with or without legs) can be worn or carried on the body elsewhere than in the hand.
The key to understanding this issue is to recognize that an Eldritch Cannon is explicitly an object, more specifically
a magical object
rather than a creature.
As an object, the Eldritch Cannon doesn't work like a creature.
The rules on creature movement and creatures occupying spaces don't apply to objects. The rules don't expect players to engage in complex inventory-management or to supply sophisticated reasoning for carrying or navigating objects in the ordinary course. Objects, even sizable ones, can be borne about the body in any number of ways. A hat or helm might be worn atop the head, or secured by a chin-strap to dangle behind the head, or affixed to a belt, etc. A backpack or shield might be larger than one's torso, and yet they can be slung over the shoulder by a strap, or carried by a hand holding that same strap. A shield can even be strapped to a backpack. When a creature goes to pick up a backpack, we don't ask whether it's problematic that the creature is moving into the backpack's space. When the creature is carrying the backpack, we don't suppose that the backpack wouldn't naturally remain with the creature when the creature moves.
As an object, a Tiny cannon does not occupy its space. The requirement that an artillerist must
create a Small or Tiny eldritch cannon in an unoccupied space
does not mean that all such cannons always occupy their spaces. The rules specify that
a Small eldritch cannon occupies its space . . . .
Absent that specification, a Small cannon would not occupy its space. So we know that if the designers wanted a Tiny cannon to occupy its space, they would have said so.
The liberal wording of the Eldritch Cannon ability offers an artificer latitude in shaping the cannon for convenience and portability.
The Eldritch Cannon ability says
When you create the cannon, you determine its appearance and whether it has legs.
That statement gives an artillerist maximally broad power to give a cannon almost any form imaginable. The only limits are the ones set out in the ability regarding size and legs-or-no-legs. An artillerist could create a cannon in the form of a hat, or a brooch, or a ham sandwich. If the chosen form is one that common sense suggests can be borne about the body, then the cannon can be borne about the body. The ability's statement that
a Tiny [cannon] can be held in one hand
(emphasis added) does not mean the cannon must be held in the hand. A cannon in the form of a hat could be worn on the head. A cannon in the form of a brooch could be pinned to clothing. Silly or not, it is a rules-accurate proposition that a cannon in the form of a sandwich could be clamped between the teeth. Heck, a cannon could be given a form that includes integrated straps, buckles, etc., for the very purpose of wearing it.
Finally, it is correct that a cannon with legs cannot move itself into an occupied space -- but only because the ability description says so. If the ability did not say so, there would be nothing to preclude a cannon from moving into an occupied space. By the same token, nothing prevents the artillerist from picking up a Tiny cannon and placing it on her body. Again, if the cannon were any other Tiny object, such as a glove, a key, or a lantern, we wouldn't think twice about letting a creature pick it up and wear or carry it around, moving from place to place with it. So there's no basis to say no when the Tiny object is an artillerist's cannon.