The empirical approach described above is a good one. Find a used cartridge that you're pretty sure will be too long. Try the local bike co-of if there's one near you. You're not going to ride with it, so it doesn't matter if the bearings are bad, provided that the threads on the cups are in good shape. Install the "test cartridge" in the BB shell and bolt the crankset to it. See how much clearance you have between the inner ring and the chainstay. You want at least 2mm of clearance, but probably no more than 4mm.

As an example, say you install a 127mm cartridge and have 6mm of clearance. (You can use an allen wrench as a feeler gauge for this.) In that case, you want a cartridge that's about 3mm shorter on the drive side. That means it will also be 3mm shorter on the non-drive side, or 6 mm shorter overall. Remove the test cartridge and replace it with a 120-122mm one that you've purchased new.

Don't worry about precision too much--there's a fair amount of leeway here. When in doubt, it's better to go a little short than a little long. If the inner ring is too close to the chainstay, you can always increase the clearance by adding a 1 or 2mm spacer under the drive side cup. But if it's too long you have to live with it or get a shorter spindle.