You could use canola oil, olive, sunflower, soy etc.
I would stay away from the baby (mineral) oil... it's a no-no for most people who make B&B. You could get throw off a lesser soap forum for just mentioning mineral oil-ROFLMAO!
Here is a quote from Indiana Soap works about mineral oil:
Mineral oil is a by-product from the refining process of fossil fuel, such as gasoline. Fossil fuels were formed in the earth, beginning millions of years ago, from decaying plants and animals. The organic chemicals in their bodies are the source of the petroleum products we use today. Products containing mineral oil, petrolatum or petroleum jelly are said to have negative effects on hormones and the skins ability to breathe, attract moisture and detoxify. It can also slow down cell renewal. It is not easily absorbed into the skin, but if absorbed, it is broken down by the liver and when it reaches the intestines, it pulls water and vitamins from the body. Mineral oil can be found in such things as baby oil, most commercial and many handmade creams and lotions, lipsticks, lip balms and even certain foods and vitamin/mineral supplements. Even though mineral oil is natural, the methods used to purify it are not. I am leery about using it on my body or eating foods containing mineral oil. I choose not to use it in my products to be on the safe side. I encourage you to do your own research and come to your own conclusions.
The is how I whip shea:
1) Melt your shea & oil & fragrance in a double boiler or microwave.
2) Pour this mixture in a medium size metal bowl.
3) Place your medium sized metal bowl inside a larger metal bowl.
4) Fill the larger bowl with ice & some water, you have just created an ice bath. You need your mixture to go from hot & melted to cold fairly quickly.
5) Whip it good on high for approx 9 minuted depending on the speed of your mixer.
6) Spoon into jars quickly before the mixture sets too firm.
It is hard to know when it's ready, if you fill your jars & later the whip falls like a souffle, you did not whip long enough, remelt & start over.
If the whip is too firm to spoon into jars, you whipped too long, remelt & start over.
Most people do not use an ice bath, they whip for 3 minutes then put it in the freezer for 3 minutes, then whip for 3 minuted & put it in the freezer for 3 minutes & so on untill it's firm enought to hold a peak.