Took apart an old cup-and-cone BB with a square axle, and the components were just totally wasted, especially the axle. Want to replace it with a sealed unit, since it seems simplest and most economical.

The old axle had "3P-B" printed on it. According to Sheldon, a 3P has a shell width of 68mm, and the symmetrical equivalent would be a 122mm. Can I just slam a 68 x 122.5mm Shimano sealed BB in the bike and get it rolling again? The only difference is that the left crank would be sticking out a hair more than it used to?

Any tools I'll need besides the BB-22 and a large crescent wrench?