Yes you can, but it won't be faster
If you created a shape like a 5-foot cube of water, and engulfed your animal companion within then, yes, then they could use their 60 foot swim speed within. It would however not do them any good, as the cube is only 5 feet large, unless you also moved the shape.
Normally turn order to move the shape could cause problems, but not here as primal companions act on your own turn, so it should be possible to simultaneously move the shape and the companion.
HowHowever, how fast can you move the shape? This is explained in the first bullet for the effect:
You instantaneously move or otherwise change the flow of the water as you direct, up to 5 feet in any direction. This movement doesn’t have enough force to cause damage.
So you can animate the shape, and move it around, but only five feet per roundeach time. As your companion can already move five feet per round when out of water, this will you not gain any speed up.
The "animating at your direction" of the shape has nothing to do with movement across ground. It expresses the idea that if you choose the shape of an animal, for example a goose, that it would not be static, you could have it flap its wings, move its head etc. The animated shape is not a creature, and does not gain the creature's statistics like movement speed.