The risk is most likely very low since the plant is in a 'dying down' mode coupled with ever decreasing cold temperatures. A virus doesn't act like a flash fire; rather, it moves slowly over time throughout the plant. If the cut is made at 7 or 8 cm, about 3 inches, chances are the stem would be completely dead before a virus ever made it to ground level. I'm making the assumption that a virus dies as soon as the host dies.
As far as botrytis in the late fall, that's quite natural and usually harmless because it is so late. Botrytis is ever present anyway, being a natural part of the eco system cycle. A typical general fall clean up should be all that's required without much fuss. In the early spring, I spray the entire garden surface with Bonide copper fungicide just around the time the noses start popping up and water it in, or apply it just before a predicted rain.
For the record, I usually make 3 passes each fall removing fallen stems, etc., the last pass being around Christmas time. If a stem is still tight at that point it stays in until spring. After all tree leaves have fallen, I use a gas powered leaf blower to blow all the unwanted stuff out, including the old summer mulch. That all gets burned.
