Pure carbon and pure silicon shouldn't do anything too strange under irradiation. BUT with many irradiation experiments it isn't the primary material that may become activated, but the trace contaminants. For example, cobalt-59 is a trace metal in many alloys not by design, but because of limited purity. When irradiated with neutrons it becomes cobalt-60 which is a strong gamma emitter. This is one of the reason that materials used in the nuclear industry tend to have much lower impurity concentrations.
I would suggest you start with a small sample of both the graphite and the silicon glue. Do a couple of short irradiation and check for radioactivity of your sample. If you have access to a detector capable of determining the energy spectrum of the out coming radiation you could do gamma analysis to determine what in your sample is becoming radioactive.
If you only irradiate a small sample of each for short times the activity will be low enough to be safe, but high enough to detect before you accidentally make a strongly radioactive sample. If you do make something that is more radioactive then you would like to deal with, just wait it out, the higher the activity (for a given amount), the shorter the half-life of the isotope.