"Wanderful. Wanderful". I grew up with many Sundays at Grandma and Grandpa's house with good ol' Lawrence and crew on TV. For a young kid, it wasn't my cup-o-tea by any stretch. Too bad in some ways. He had great musicians. I always wonder about those guys/gals in the background. Not always getting their names mentioned, but a real honor to go through life telling your grandkids, or new friends, that you were in Lawrence Welk's band on TV. You had to be good.
Back to your question, I can only give an opinion (no professional first-hand knowledge) as you requested. I would say most is live takes, with some occasional editing as necessary. The magic of TV. The link below has some actual mistakes when Lawrence or a performer speaks a word incorrectly during an introduction and then repeats the word correctly. They could have edited it out and the introduction redone but did not. There is no reason to doubt that this show could have been done in one take. After all these are real professionals involved. On the other hand, with TV having timing constraints for commercials and 60-minute time limit, they may have had to use some editing as needed. So they could easily set up each song as a take, and do the intro's separately. Bottom line....I believe this was
mostly done in one take, but I don't know for sure. On the other hand, today, the production would probably be heavily edited just because that's how it would be done today.