An isolation transformer provides some safety, but it is limited. Once you attach the ground clip from a grounded scope's probe, the power supply is once again ground referenced. In this arrangement, the isolation transformer makes the circuit safe for your scope's first probe, but not for you.
Also note that any other probe that you attach has to have its ground clip attached to the same place as the first probe's ground clip.
A differential probe is not cheap, but reduces the complexity of what is or isn't safe to probe. It makes probing with the scope as straightforward as probing with a DMM as far as isolation goes. The Micsig DP10013 probes are probably the most reasonably priced ones for the supported bandwidth. The EEVblog probes are quite a bit more expensive, but have a 10X mode which is great for general use.