I had to do something similar with my big 1945 GE roaster. As long as you didn't disturb the asbestos, you should be OK.
My mom had a mid '40s Nesco about the same size as your unit. It worked fine, but made an odd crackling sound for about half a second as soon as the heating element was activated from a cold start. It was just a little too primitive for me so I let it go. I have a later Nesco of the same size that has a newer, safer heating system.
Can you share details on the burned wire? Did it just need to be re-attached to a terminal?