I know that cooking sticky rice uses a steamer setup. But do you need a rice cooker to cook sticky rice property, or can it be done using regular kitchen tools, e.g. pots and pans?
Rice cookers are not magic. They do not do anything, for any type of rice, that cannot be done with a more traditional pot and heat source.
What makes a rice cooker effective at what it does is that it has a thermometer measuring the temperature of the pot, at least at the edge. This allows it to detect when all of the water has been absorbed, because only then can the temperature rise above the boiling point of water. The logic or circuitry built into the cooker than shut off, or change the heat level to warming.
So of course, with experience and good technique you can cook anything in a regular pot that can be cooked in a rice cooker, including sticky rice.
Did you mean to ask how to properly cook sticky rice with traditional equipment? You can google a myriad of recipes. The common theme appears to be soaking and steaming (as you mentioned), for best results. For example, this one from Food Network requires no rice cooker.
Sticky rice, or sweet rice, is different from rice typically used for sushi. I can be cooked in a rice cooker. However, I find that I prefer it steamed. My method is to cover the rice with water and soak for a few hours. I don't have a traditional cooker, so I place in a kitchen strainer, then put the strainer in a pot with a couple of inches of water at the bottom. I place a kitchen towel around the rim of the pot and then a cover. This retains much of the steam that is produced. Steam for 20 minutes. Then I flip the mound of rice in the steamer (much like I would flip a pancake in a non-stick pan), re-cover and steam for 5 more minutes. Perfect sticky rice.