Does anyone manufacture a seatless bicycle?
Most trials bicycles are designed without a seat.  However, they are likely to be uncomfortable when ridden for long distances.

You may want to consider what what you mean by "stay fit".  Fitness must have goals to be obtainable.  Cycling is generally consider to be cardio exercise that improves aerobic fitness.  Standing while cycling is more of a strength training exercise that is less maintainable over time.  I don't know of any manufacturers that produce a bicycle meant to be stood on all the time and intended for distance.  It's not something people try to do often, so if their is one, it would be very small, selling to a niche market.