Here is a good way to have multiple speeds on a bike without using a derailleur. This bike has two gears on either side of the front sprocket, and a driveshaft for each of them. One driveshaft would be disengaged while the other was engaged. the driveshafts engage bevel gears on the rear wheel. This might be a little heavy, but should work just fine.
Other driveshaft drives were patented in 1897 with a transmission and a gear shift knob and in 1891 with a single drive shaft. Alexander Pope also patented a driveshaft bike.