Thanks for all the advice! It's a steel frame, and we are leaning toward special-ordering a wheel that fits instead of the cold-setting option (though apparently the guy who would do it is quite good).
But based on what y'all have said, we'll probably make sure to measure with the wheel off, and on the off-chance that the frame has already been cold-set once in the past. Will let you know if anything interesting comes of it!