I made a 100% cocoa butter soap once, so yes, you can make a soap with 95% hard oils. Just be aware you probably won't have time for any design elements, like swirls. If you want to color, I suggest you add the color to the lye solution (such as indigo or alkanet, for example.) If you are okay with 20% cleansing, your oils will give you that, but for my skin, I'd use less of the two cleansing oils (PKO & CO) but that's me, it just would strip my skin of my natural oils and leave my skin feeling rough & extremely dry. But I think you live in a more humid climate, so it may be fine for you (I don't know.)
And as Dawni said, butters in high amounts are said to inhibit lather, so maybe add some sugar or sugar containing liquid to the mix, but maybe not. PKO & CO contribute to bubbles & lather, so perhaps you won't need a sugar boost. But if you have access to aloe juice, you could use that for making your lye solution and get that little extra boost of sugar that way. It's up to you; I'd try it either way with or without the extra boost just to see what happens.
Also, since this is an experiment (anything new is an experiment, right?), I suggest you make a very small batch. Something along the lines of 300 to 350 grams of oils. I'd keep the lye concentration to about 33%. And I probably would not insulate because it could lead to overheating and cause the soap to crack on the surface. So keep an eye on it if it is a single loaf-type mold & if you see cracking start at the surface, put it on top of a cooling rack to introduce air-flow to the bottom surface.
It may be hard to cut, so you will have to cut it early rather than waiting too long. Maybe individual molds would be a good option here, otherwise you will really have to pay attention to how soon to cut into bars from a single mold.
How many batches of soap have you made? If this is still your first batch, it may be a bit challenging as a starter soap because when we start out we tend to be slower & more hesitant in our actions simply because it's a new skill we are learning. In other words, making soap with mostly hard oils can be more difficult for a beginning soap maker simply because the learned skills are not yet well established. For a beginning recipe, I would suggest something with about 60% soft oils in order to allow the extra time so the beginner can get used to the process. But you can choose to start with a more difficult recipe, if that's what you want to do. I didn't always try the easy route as a beginner, either.