That kind of depends... if you're covering gray you definitely need the oil in the scalp, I've seen it time and again in my own head when out of impatience I co-washed the day before as for me 2-day hair is better. When I didn't wait, especially in the winter when oil production is slower, the color didn't take as well in the new growth even if I left it on longer.

As for no products, maybe just a moisturizing cream or leave-in, which at the same time might give you a light hold will do, the chemicals in hair coloring are more than able to penetrate those. Or try
a bit of jojoba or coconut oil, or even aloe vera gel. And... you can always wear your hair up for a day, for heaven's sake...