If my experience with a few of my New 3DS SNES ports meant anything, I can tell that Super Mario Kart would run fine on the hardware without any input lag whatsoever. Though, it's worth bearing into mind that there's the lack of Local Wireless multiplayer functionality, and that any race will always display the actual gameplay on the top half of the screen.
I can't exactly imagine the SNES tracks in Mario Kart DS being anything but unimpressive. The problem is, these tracks were designed with the physics and drifting system of SMK in mind. Of course, most of the later installments didn't replicate these quirks and opted for literal recreation instead of remaking these tracks. It's worth mentioning that these tracks were simplistic due of the severe limitations of hardware available at the time of its original release. The end result is that they came across as ultra-simplistic and underwhelming tracks in comparison to the other entries. It certainly doesn't help that MKDS picked some of the least enjoyable SNES tracks.