CrowdSupply told me I need to have CE certification if I want to sell the unit outside of the USA, which was a bit of a setback. After spending a while failing to make significant progress figuring that out I have (sadly) decided not to sell outside the United States. If market demand is high enough I might do a followup campaign to make fully certified units, but right now its not worth it.
A colleague and I just ordered one i-prober 520 each, which are in the mail right now. Your project would have been a nice alternative. I will follow your progress with keen interest.
I have been doing UL and CE certification for my designs for over two decades. If there is even a remote chance that the product will be sold outside the EU and might require UL, I prepare the electronics for both.
CE is different from UL in several aspects, one of those is important to you: For many applications you are permitted to do your own declaration of conformity, even without consulting a notified body. For the aforementioned applications, CE is mostly about EMC. If you know what you are doing, which I imply after looking at your design's specs, you can avoid undue emissions. Looking at your schematics, as long as the analog parts don't oscillate and forwards the signal to the oscilloscope, the PIC is the only possible, quite low power, HF-source.
As far as immissions are concerned, you simply state what your device can stand. I mean, this is an EM-field probe, so it is likely to react to EM-fields...
CE for a device like yours could be covered by a simple declaration of conformity from you. If you involve a notified body, it is still you who issues the declaration of conformity, but back it up by reports from the notified body.
Another loophole was mentioned earlier: a self-assembly kit might require no CE at all.
You might even consider just shipping certain components (mechanics, sensor, PCB). Electronics and even PCB could be sourced by the buyer through the usual channels, albeit at higher cost.
Remark regarding usability: I don't care much for batteries and wallwarts. My i-prober 520 is going to be powered by the auxiliary output of my lab power supply. USB could be a feasible connector, but we might want to provide a clean power source.
From a business standpoint I think that you made a sensible decision - feel the local market and deal with abroad later. Good luck!