Yes, a positive controlled vva will eliminate a voltage inverter.
However, there are literally hundreds of millions of microwave communications systems that have switching supplies in them. They all work fine. first of all, the op amp you use has power supply ripple rejection. Find an op amp whose ripple rejection extends to 10 KHz--you should be able to effectively reduce ripple by 60 dB in the op amp alone. Then, as suggested above, do some series R shunt C filtering of the 10 KHz ripple. You should be well withing any emissions mask requirements at this point.
Also, make sure the circuit board layout around the voltage inverter is proper--no large ground loops, adequate power supply bypassing.