Kick-off Spread Spectrum Clocking
Most of radiated energy in EMI/RFI comes from the edges or clock transitions. How SSC works is by dithering these edges to reduce the reinforcement of the transmitted frequencies.  Essentially you are broadening out the peak transmission energy.  You are not really changing the energy as the integrated energy (integrated wrt to frequency) or the area under the curve in the frequency domain stays the same.  It is less "peaky" in the SSC case.

The key idea here is to have that edge transition at the same lockstep transmission but with +/- some small amount of time. The idea is that the setup and hold times of any logic is not adversely affected by this jittering.

In reality, it would be easiest to just dither your output stream.  Most serial stream protocols and implementations can accept jitter in due course.  Especially systems where there is the concept of an "eye diagram" and you actively re-align the sampling to the clear center of the eye.

In a larger system with purely digital logic, dithering the will necessitate the slowing down of the clock to maintain the same timing margins.  However, it is necessary to point out this is a very small amount of slowing down so it probably would not be noticeable.