There are plenty of federal prosecutors and judges who know how to handle classified evidence in court. I can't remember his name off the top of my head anymore, but I recall when I deep-dived into the Gitmo suspects and military tribunals a long time ago, there was a judge's name who constantly kept popping up in the paperwork of related terrorism cases. Seemed like he was one of the designated "terrorism judges" who had the clearance and authority to review classified intel and info and make determinations on what can be used and presented. I believe he is from the Virginia district courts possibly
Yes, the judge I was referring to was a district court judge in the US (I believe in the state of Virginia but not positive) who hears terrorism cases and makes decisions on whether the classified evidence the prosecution wants to withhold is actually worthy of being withheld -- i.e. if it's actually a threat to national security to disclose, and whether that national security risk outweighs the need for the defendant to be presented with all the evidence used against him to mount a defense. Also, if there is any way to present the evidence with redactions so that the defense can see it, but not reveal sources/methods etc.
Prosecuting cases that depend on classified national security material is nothing new really when it comes to the federal courts. There is a system in place to do so. The military tribunals are an entirely different beast, although some might say different sides of the same coin. I'm inclined to go with the latter, although I don't think the federal courts are quite as bad as the military tribunals in terms of fairness to defendants.