After a bit of testing, they are not 100% consistent, but it's close every time.

In the Bob-Omb Battlefield stage, there's a bit of RNG because Koopa needs to jump over rolling cannonballs and the time will not be exact every time. With that in mind, I got between `1'30"0` and `1'32"0` for the N64 version, and no less than `1'28"00` for the DS version.

In the Tiny-Huge Island stage, I got around `0'23"0` for the N64 version, and I ALWAYS got `0'26"00` for the DS version.