Vitamin E is an antioxident, not a preservative. The only thing it will do is prolong the life of the oils you use.
If you use sweet almond oil, that has a pretty short shelf life. Personally, I'd switch to coconut oil which has a very long shelf life as does the cocoa butter. Then, you really don't need the vitamin e.
A bigger concern to me is that your recipe doesn't have a preservative.
I know, I know, no one wants to use a preservative. Everyone wants all natural. However, when you're making a product with water or one that has the possibility of having water introduced, you run the risk of serious contamination if you don't have a preservative.
A scrub will most certainly have water introduced into it when people use their wet hands to scoop the product out.
You really run a huge risk by not preserving. Unfortunately, you can't see all the things that grow in a moist environment - they often times can be invisible to the human eye. So, you could be growing mold, yeast, bacteria etc.. and never know it.
I would really encourage you to rethink making an unpreserved product that is certain to have water introduced into it and that people will be slathering on their bodies.
Edited to add - back when I was reesarching making bath and body product for a business, I was told about the preservative thing and I didn't believe it.
Well, I made a batch of unpreserved lotion (which contained water) and batches of unpreserved body butter and unpreserved body scrub. I introduced water into the body butter and the scrub and left all three sitting on the counter. Within days, the lotion was moldy, quickly followed by the body butter and the scrub.
Don't chance it.
