Are Koopa the Quick times constant?
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.