Is there an analog circuit or filter that can produce constant phase shift over a specific bandwidth?
Option 1: Generate the quadrature signal of your input. Sum it with the input in the correct proportions to get 7 degrees phase shift. How to generate a quadrature signal over more than 2 decades of frequency range is left as an exercise for the reader.

Option 2: Make a 1:1 phase locked loop and put an offset in the phase detector to produce 7 degrees phase shift. How to make a good VCO that spans more than 2 decades of frequency range is left as an exercise for the reader.

Option 3: Digitize everything and let software sort it out.