The probe tip is connected to the CRO via a 10 M resistor, it will not cause any problems. Your circuit under test must have its common rail either earthed or properly floating. So get a DVM, switched to AC volts first, connect one probe to a point you can designate as earth. The earthed pin of a power socket would be a good place. With the other probe,, check the chassis voltages on every thing on your bench including the test fixture. You should get zero volts every where. If the earth is missing on a piece of test gear then the chassis will float to 1/2 mains voltage, connecting this to a piece of sensitive equipment can blow it up.
frank