Fishingfool:
I am a newbie to casting also so don't know a lot about the practical details. However, to get started take a look at a couple of websites that have useful information: www.polytek.com, www.wingnutinternational.com , www.perma-flex.com , www.artstuff.com. They offer instructional...
I don't know whether the balls on deodorant bottles are blow molded or not. However, the part/fusion lines could be removed by centerless grinding. If the balls can be solid, the entire ball could probably be made by centerless grinding. Check out website www.glebar.com who specialize in this...
It is not clear how large or what shape the part is which may make a difference in the technique you can use. Take a look at these websites to see if they are helpful. www.polytek.com, www.artstuff.com, www.synair.com.
They describe some mold making techniques and other how-to info.