Strong! uses two matched bells. Combining it with the "One" program has never made any sense to me. When you're training for strength - train for strength. Don't water it down with conditioning.
I did Strong! with double 32s which I had never done more than 1 C&P rep with. I probably could have managed two reps, but I never tried.* By the end I was doing many sets of triples with those bells, and doing so made the cert stuff pretty light by comparison. I did a snatch test right before I started the Strong! program - 4+40. I did ZERO ballistics, no cardio, no swings, no sweating, no conditioning of any kind for the 8 weeks of the program. When I got done, I did another snatch test - 4+45.
Increasing strength is its own brand of conditioning, at least until you get so dang strong that further increases require a conscious decision to specialize only in strength. Work capacity works the same way and is easily demonstrated with a thought experiment: Bob has a best 1-arm press of 40 kilos. Tom has a best 1-arm press of 28 kilos. Who can do more press reps (more work capacity) with a 24? Obviously, the same holds true for any lift. So, if you drive your maximal strength up by spending a good long time focusing on it, everything you do with a lighter weight will be easier, more "sub maximal". This equals greater endurance.
So, yes you can do it with 2 matched bells on the road, and for the reasons I stated, do the conditioning component some other time. I'd wager you'll be quite surprised how tenaciously your current conditioning level stays put while you do.
* This is NOT what is recommended in the program, but I don't regret starting heavier than recommended.
