Unless specified otherwise on specific records we allow lowest time possible by any means neccessary including glitches like messing up the timer to start later and shortcuts like leaping across/through areas as long as it's verifiable.

No Shortcut implies that you take the full intended path right through to the end assuming that there's only one obvious path to take.

Koopa Races is to race from the natural starting point to the natural finishing point, no jumping out further to start.