This is a frequent problem with small engine-generators. Caterpillar used to have data sheets online for most of their generators - maybe that's changed. If the company is still in business you should be able to track someone down in the engineering department who can find the data.
For arc-flash calcs per IEEE 1584 equations, you really only need the subtransient reactance and the transient reactance - along with the X/R ratio, which can be calculated from the winding resistance and the reactance values.
One option is to find data for a similar generator (kVA, voltage, rpm) and use that. Just state what you used in your report. When calculating arc-flash for scenarios running only on a local standby generator, the fault current is generally low, resulting in long clearing times. If you're estimating, you are better off estimating on the low side (fault current) (or high side if you thinking in terms of reactances. SKM has typical reactances for generators, but I wouldn't trust this data for arc-flash calculations.