Ordering and swapping a single garage door panel yourself is possible if the door is a common modern size and the track hardware is standard, but on a door built around 1957 that's often not the case. The panel dimensions and hinge spacing on a door that old frequently don't match current stock sizes, and you won't know that until you've already bought a panel that doesn't fit.
The part we'd flag hardest: the door's spring stays under load the whole time you're working near it, even with one panel off, and that's not a place to improvise. If you're comfortable sourcing a panel that matches your door's actual measurements and you're not touching the spring or cable, a DIY panel swap can work. If either of those is in question, it's worth having someone confirm the match before you cut into the old section.
We're honest that not every panel job needs a truck out from Yorba Linda - sometimes a local handyman with the right panel in hand is the cheaper fix. We'd rather tell you that than take a job that doesn't need us.