Agree 100% with Janne.
Never use a non-isolated scope (almost all of them, except things like Fluke Scopemeters, Tektronix THS7xx series or Tektronix TPS2xxx series) without proper ground connected. It's not just the BNC ground shell that would become a shock hazard, but the whole scope is designed with the idea that ground is a safe potential, so no attempt was made to isolate the user from it. The case might be connected to ground, or the isolation between the knobs/buttons and ground might be bad.
Depending on whether you want to measure the voltage or current waveform, the correct tool is a high voltage differential probe or current probe. High voltage differential probes are also made by companies like Tektronix, and also cheaper alternatives like Testec, but it's going to be expensive regardless. For current probes, you should be able to get a relatively cheap one because you only need AC, and not a lot of bandwidth. Should be possible for under $100 used, probably more when new.