You could use a vacuum sealer in theory, but I'm not sure how well it would work in real life. I have one and use it a lot for food storage, but I don't use it for my soap or other products.
A home type vacuum sealer that most of us have needs a bag that has some kind of texturing inside so the air has a pathway out of the bag during the vacuuming step. The texture tends to make the bag translucent; shrink wrap is transparent. To get be able to use clear bags, you'd have to go to a commercial vac sealer and that is a lot more expensive than a home vac sealer.
A vac bag is usually made from heavier duty plastic than a shrink bag to guard against pinholes and imperfections in the plastic. If you use a light duty bag for vacuum packaging, it often fails to hold a vacuum. You end up with a heat sealed bag, sure, but it fits loosely around the item, not vacuumed down tight.
Also, a vac sealer won't shrink the bag into a wrapping that fits the item like a glove -- the plastic just compresses down flat however that happens. You can guide it a little so it flattens smoothly, but it's not going to be a form fitting cover.
