I know this sounds cruel, but We'll try to make it as cool of an experience as we can for the little canine.

The punting vehicle, also known as the Perruna Balloona, is a double sphere of clear plastic.
The inner sphere (about 18" diameter) has a textured track that the Chihuahua can use to turn and steer the Perruna Balloona. It is accessed by a cylinder with an inner sphere vented closing hatch.
The outer sphere is also of clear plastic and has elliptical cup shaped fins along its prime meridian. The space between the inner and outer sphere is filled with helium.

The Perruna Ballona is about 4' in diameter and will be punted by the Human Impeture and then the Chihuahua takes over.
The Chihuahua will try to right the yaw and roll by precision placement of steps along the textured path along the meridian.
Once the Chihuahua does this, He or She begins the Hampster Wheel part of the Flight by rotating the Perruna Ballona and causing the cup fins to further propel the craft.

The landing should be nice and gentle, considering the Helium and the Human Punt Catcher at the other end of the track. (The Scooby Doo theme song will play for the duration of the flight).

(I don't know if this was already posted here, but I was inspired by an anno of [waugsqueke]'s on Dachschund Luge - I know it's mean, but I hadn't laughed aloud, for real, for months before reading that anno.)