Vitamin E is not a preservative. It is an anti-oxidant. An anti-oxidant will slow down the rancidity of your oils. A preservative prevents the contamination of your product by things like bacteria, yeast, or mold. Vitamin E will not prevent contamination of your products, but it will retard the rancidity of the oils in your products.
A review of rancidity and anti-oxidants
A more in-depth look at anti-oxidants
You do not need to add a preservative to a product that doesn't contain water (anhydrous products) unless it will come in contact with water. (Something that you'll take into the bath or shower with you will come into contact with water, so you will need a preservative for those products.) You can add an anti-oxidant to the product to retard the rancidity of the oils, but you don't need a preservative in something like a whipped butter or balm.
Preservatives - a whole bunch of posts on the topic
Why use a preservative?
Mechanisms of rancidity
Storing products in the fridge
If you really want to make products without preservatives...
The importance of preservatives
Anti-oxidants retard the rancidity of your oils.
Preservatives prevent contamination.
You need to use a preservative in a product that contains water or will be around water.
You don't need to use a preservative in an anhydrous or non-water containing product.
You can use anti-oxidants wherever you are using oils.