Noise on my oscilloscope when probing a wire
200mV is rather large. It is possible that it is just being picked-up by the antenna formed by your probe connection, but unless you are in a very noisy environment that might be unlikely. It could be that your oscilloscope is defective.


Use a BNC termination block directly at the oscilloscope input, is the noise still there? (If you don't have one you can build one by soldering a 50Ω resistor directly inside a BNC connector, alternatively you can just insert a very short piece of wire (e.g., a piece of a paperclip) to short the connector.
If your oscilloscope can change the bandwidth (e.g., from 100MHz down to 20MHz) is the magnitude of the noise the same? Is the noise reduced by more than \$\sqrt{5}\$?
Is the noise the same for both channels?


Those would all be indications of a noisy input stage or sampling stage to the oscilloscope channels.

If shorting the input directly at the connector removes the noise, then environmental noise is your problem. You would probably have to look into how circuits are grounded and what antenna loops are present in your measurement setup.