DC-DC step up from 3V to over 100V
Avoiding a transformer to keep the circuit small ... doesn't work so well. 

See Spehro's answer : to avoid saturating the inductor in a flyback convertor, you need to keep the current low, or use a big inductor. The problem is that you are storing energy in the inductor core at low voltage, and releasing that energy (in a fast pulse) at high voltage. And it will only hold so much energy before it saturates.

With a transformer, while the primary winding is storing energy, the secondary is already pulling energy out (at higher voltage but lower current) so very little energy is actually stored in the core. This means you can transfer much more energy for the same size of core. Or use a smaller core for the same power delivery.

Something like this might be close to what you want, about 1.6*1.6*1.6cm to deliver about 6W (0.06A at 100V). You could drive its 3.3V secondary from an H-bridge at 100kHz and extract power from its primary, with a bridge rectifier made from those fast diodes. Or wind a custom transformer on a core like this or this smaller one to get exactly what you need. I haven't done the math to design a 10W supply around either of these cores. It may be better to look at application notes for some of the ICs you mentioned for guidance on winding suitable transformers.