So the search term you are looking for is frameless iPhone Mini case. Try that on Google, Amazon, eBay, and AliExpress. These have no side protection and use the iPhone's native buttons. BTW, yes, all Apple first party cases use added buttons for all except the alarm/ring silence slider but they preserve the clickyness of bare buttons generally (I have selected demo ones in the store over new in the box ones because they were not as clicky).
The other possibility for you is to search for minimalist cases. These can be as thin as a fraction of a mm and basically only offer some scratch protection. None that I looked at would meet your need for eliminating the camera bump.
I now have 5 iPhone Mini cases waiting for my new iPhone arrival tomorrow. I really want to make the Mini as narrow as possible for my short fingers for one handed use. I came up with the idea of modifying a case to remove the side protection (95% plus of all drops hit the corners only), only to discover several days later the idea wasn't original. The best implementation of "frameless" is the Rebel case (search for videos with 50 ft drop tests) but not available yet for Mini (and the company is notorious for being unresponsive).
I did get two frameless covers, but both are highly unsatisfactory to me, really only providing scratch protection, not drop protection. So I'm going with my original plan to modify a full case, at least until Rebel becomes available for the Mini.
Another idea for you is to buy a Magsafe cover and cut off the entire frame. I'd bet between the camera hump and the magnets that it will not shift uncomfortably while holding it. Then you would have exactly what you want!