Hiding rain drain pipe below the sidewalk
Why don't you move the end a little further uphill and empty the pipe into some kind of culvert drain or splash block that slopes down to the curb?



Or you could use a pipe fixture like this:



There's a brand name behind that thing (Mitered Drain), and I'm not sure there are identical alternatives, so I'll go ahead and identify the brand. I'm not their spokesman. They just have the solution that's identical to what came into my head when I saw your question.

Or maybe you could transition to a rectangular section of pipe: