Hi, Ameya. I usually put a few spritzes of rubbing alcohol into a bowl or cup and then add my oxide and mix it into a slurry. I add a couple more spritzes of alcohol if it's still too dry or clumpy. I like it pretty liquid-y before I add it to my base. Then I stir it well with my base and spritz the surface with rubbing alcohol again before pouring. Even with careful mixing, I may get a speck or two of oxide show up in my soap, but it is minimal. (Come to think of it, I think I remember seeing a couple of specks with the ultramarine violet oxide, too.)
I hope that helps! Best of luck!