I have to give Hunter credit for stimulating this idea, and it is entirely possible that others have said this - apologies in advance if I am stealing your idea.
But, it seems to me that Democratic politicians can routinely shame Republicans for their use of the "I am not a scientist" dodge.
What they need to do on every question in debates and with reporters is to sarcastically preface their answer with the appropriate "I am not a XXXXXX" where XXXXXX is the professional that would be appropriate in that context.
For example:
If asked about the spread of Ebola and what we should do about it, every Democrat should answer with, "Well I am not an epidemiologist, but, in reading what they have to say, I understand that there is very little likelihood of the Ebola virus spreading in the United States on the scale that is has in Africa. Of course prudent measures can and are being taken to minimize the risk of Ebola becoming a significant problem in this country. Furthermore, this event points out the real need for our government to fully fund the efforts of the CDC to identify and create appropriate responses for us as a nation to diseases such as this. Ebola could mutate and become much more virulent, but even if it doesn't we know for a fact that there will be other epidemiological threats to us in the future and it is unconscionable that we seek to balance our budget by cutting funding for such programs."
Similarly, if asked about climate change, begin the statement exactly as the Republicans do with:
"Well, like my Republican colleagues, I too am not an expert on climate change. But I have read extensively the work of those that are and there is now widespread agreement that the global warming - it is an indisputable fact - is occurring because of man-made sources of greenhouse gasses, largely the release of CO2 into the atmosphere from our burning of fossil fuels. Given the enormous consequences that continued warming would have, it seems prudent to me that we should immediately seek to reduce the CO2 emissions of our entire civilization. I strongly support research into ways to cut greenhouse gas emissions and I think that it is time that the United States showed leadership in this regard by aggressively reducing our emissions through voluntary AND governmental actions. The time for talk is over and the world needs action soon or it will be too late."
You get the picture I suspect. We can turn their science denialism on its head and make them look like the idiots that they are. To be sure this will piss off the creationists and the climate-change deniers, but they weren't going to vote for us anyway.
When asked about ISIS the answer could be:
"I am not a military expert, nor am I an expert on the politics of the Middle East. However, we need to make a political decision as a country whether or not we want to continue to continue the failed policies of George W. Bush or adopt a new path forward. History shows us that we are not well received over there. The instant we get involved, sworn enemies join together to fight against us. I realize that there are complex geopolitical factors involved in this, and I am not in favor of an isolationist policy. But we have to prevent a continual recurrence of the events of the last decade, and the only way to default to a policy of leaving the Middle Eastern countries to sort it out for themselves."