Usually you'll incorporate some of the other sign in your personality. Since only a minute would make a difference for you, you'll want to make sure that the time is accurate (this mostly makes a difference in aspects because it'll change house rulers). Mothers (and hospitals) can be wrong by a minute! You'll want to keep track of aspects made to your Pluto (ruler of Scorpio) and Jupiter (ruler of Sagittarius). If you're a Scorpio rising, Pluto rules your 1st house so aspects to him will be very significant, especially impacting your overall personality and physical self. For Sagittarius rising, it would be Jupiter that would be more significant.
Scorpio rising:
http://www.astrologycom.com/scorpasc.html
Sagittarius rising:
http://www.astrologycom.com/sagasc.html
Cancer sun with the 12 moon combinations:
http://www.astrology-numerology.com/sun-moon4.html