Quick-and-easy initial check -- look inside the cabinet and count the transformers? One output tranny for the speaker (smaller) and hopefully one (bigger) power tranny. If you only have the one transformer, then it's a hot-chassis series-string setup. Just to verify, check the tubes. Is there a rectifier tube (5y3, 6u4, etc) and what type of output tube? If you see a 6v6 or similar, you probably have a power transformer. If output is something like a 35c5 or 50l6, then it's a series-string.
Based on the age, type, and "bargain-bin" status, I would be willing to bet it's a hot-chassis. The good news is that adding an isolation transformer to make it safe is a trivial modification and not very expensive.