When using a reamp box, i'd suggest recording a mic on the cab as well as the DI at beginning, then when you go onto the reamp stage, then you can blend the new mic/amp with the old mic'ed track... blending the same signal through different amps is great, it gives such a fat tone!
Another thing to point out, is that if done correctly (and using a high quality DI and reamp box), then there will be no discernable degrading of the sound, nor will it sound strange- it really is a great way you can use to get a perfect take, and then a perfect tone later :)