You can measure for opens and shorts with a resistance meter, but to really check an output transformer, in my experience, you will need to be able to measure impedance at audio frequencies. Such meters exist, but they are not all that common.
In addition, most output transformers have high Voltage running through them, so at some point, they may need to be checked at operating Voltage to make absolutely sure of them.
Again, this is just my experience working on guitar amps and commercial amps which use output transformers to drive 70.7V and/or 25V speaker lines. Someone else might have some nifty, easy way that I have not run across.
Having said that, I have to wonder if it wouldn't be more lucrative to just see if you can get the amp running, then sell the running amp? It would take some research on your part to determine what such an amp would fetch on the market, but I would have to think it would be more than just the output transformers would fetch as "pull-outs". And, your problem may not be all that difficult to solve. For instance, many, many Marshalls used two fuses, one for the "Mains" and another for "H.T.", or the high Voltage supply.
And, even if you don't want to work on the amp, I would expect you could still get money for it "as-is", if you can locate a buyer who is into working on older guitar amps.