Does anyone know of a microcontroller/DSP with no clock speeds or any oscillators in excess of 1.705 MHz?
Many microcontrollers are fully static, i.e. that the clock can be completely stopped, or that you can run it at frequencies like 0.1 Hz, for instance, for 1 instruction per 10 seconds (might be useful for debugging). Some components on the die may require a minimum clock frequency to work, however, like an ADC: the sampling capacitor will discharge if you don't complete a conversion within a certain time.

That being said, the controller's clock will cause EMI over a band much wider than just the clock's frequency. The shorter the rise/fall of a digital signal the more energy there will be in the harmonics. To decrease EMI some microcontrollers, like Freescale's MC9S08, have (switchable) slew-rate controlled I/Os.