Your camera produces an image in the aspect ratio 3:2 (or 4:3, if you use a four-thirds camera). But why not let go of that, and use your own ratios?
Or like wide.
I am a firm believer in “make the picture whatever shape you think fits the picture best”. Not “whatever the frame-makers in China or the paper-makers in Switzerland have decided for you”. Make the picture the way you like, and then cut white edges off paper, and have custom frames made.
On that note: no, you cannot print a 4:3, say, on 3:2 paper without either cropping the picture or cutting off white edges. It’s the reality of life.
I have found that often, people do not understand this: “yes but I want my 4:3 picture to fit on this 8:10 paper and no, I won;t accept cropping or white edges”. Well, here’s news: you have to. To understand why, imagine you have a square picture. Try fitting that on an 8×10 piece of paper, and now you will see why it cannot be done. So you either crop to the paper aspect ratio prior to printing (Lightroom is very good at that), or you print with white edges, which you then cut off. It’s one of those “it is what it is” things.