I don’t have much knowledge of country music history but since you have no answers and this type of string writing transcends genres I’ll tell you a bit about the strings on these recordings. Both songs are very different in the way they use the strings.
“Welcome to my World” contains a string orchestra of first and second violins, violas and cellos. There isn’t a standard number of players used for string recordings, it is up to a combination of the arranger/orchestrator, producer, studio size and budget. Usually a recording string section will be smaller than one in a symphony orchestra but the proportions of players are similar. A typical set up may be 12 or 16 violins split between first and seconds, 4 or 6 violas and 4 or 6 cellos. There could be many more or less players based on the factors I mentioned earlier. Basses are sometimes used but not nearly as much as the others and I don’t hear any here. If you listen with headphones you will clearly hear the violins are all panned towards the center and the lower strings more to the right. It is not hard to pick out the low and high string sections throughout the song. At the very end of the song you can hear the high strings play a line and hold their note then the low strings play a descending line to finish the song.
On “I’m Sorry” there is only a single section of violins. If I had to guess I would say it is about 6 to 8 players. The string arrangement is much simpler, the strings only play high unison lines, usually as a call and response to either the vocal or the chorus. There are no lush chordal passages like on the first recording. In this case the string section is treated more like a single instrument playing melodic accompanying lines.