Elvis obviously used a basic 3 or 4, maybe even 5, chord technique when he played rythmn on his first Sun recordings - it was essential to that 'Rockabilly' sound. Plus, they were the only chords he had learned to accompany himself on guitar since a very young age.
I personally feel that Elvis did progress as a guitarist over a fourteen year period but because of all the movies in the 1960's period most of his basic guitar work was confined to miming on a studio soundstage. In 1968, with the dawn of the classic Comeback Special, the sit-down shows were very much an eye-opener because nobody had ever seen Elvis play his guitar with such conviction, apart from his bass-rythmn licks on his early TV Shows. At this point, I am reminded of one his most raw rythmn guitar-strumming techniques used on the raucous performance of "Money Honey" on one of the final Dorsey Shows - fantastic! But, the 68 Comeback linked into his Vegas 69 Comeback to the concert circuit and the wonderful blues of "Baby, What You Want Me To Do" - a stool and an electric guitar was primarily needed for this. This raises a question of my own, which is: During this segment did Elvis play electric rythmn on Del Shannon's "Runaway" as he did on the medley "Little Sister"/"Get Back"?
In the studio, I do believe that Elvis was playing acoustic guitar on other songs such as "Shoppin' Around", "Like A Baby", "Reconsider Baby". The later sessions include "From A Jack To A King", "Stranger In My Own Home Town", "If I'm a Fool (For Lovin' You)" and a number of studio rehearsals for "Elvis-That's The Way It Is". Plus, he played electric rythmn on these rehearsal jam sessions too.There are possibly a number of other songs too from this period and I'm sure the other fans will point these out or even correct myself in some of the songs that I've mentioned. Finally, "Blue Christmas" springs to mind as another classic number that EP played acoustic rythmn on between 1957 & 1977, both live and in the studio.
I can't recollect EP ever playing guitar on "C.C. Rider" or "I Got A Woman". I think whilst he was singing "C.C." at the start of his live shows in the seventies he might have adopted a simple 3-chord technique to strum along to on James Burton's lead instrumental parts. And, whilst EP was no Hendrix or Clapton, he did symbolize the guitar as an essential image of rock music in his stage show.
A classic quote: "There's been a big change in the music field in the last ten or twelve years...and, I think everythings improved - the sounds have improved, the musicians have improved and the engineers have certainly improved..." - EP, Burbank, 1968.
I hope this helps.