Waltz, by definition, is music played in 3/4 time. Literally the only thing that defines the word "waltz" from the standpoint of music is its time signature, 3/4. So calling something a "4/4 Waltz" is a contradiction in terms.
That being said, you can absolutely give your students Waltz choreography to 4/4 music, to the counts "slow-quick-quick". There are certain pieces of 4/4 music (especially certain ballads) that don't really qualify stylistically as, say Foxtrot or Rumba, and where one might prefer to dance in the syllabus and style of a classic Slow Waltz. And even though it may be little more than an issue of semantics, I would advise against calling it Waltz outright. To anybody who knows better, you might come off as not totally educated on the matter, so you're better off describing it as exactly what it is -- Waltz choreography danced to 4/4 music.
Incidentally, "What a Wonderful World" is either in 12/8, or at least has a strong 12/8 feel, which can be somewhat awkward for Waltz box-like actions taken to SQQ timing. For social dancing I would recommend either some sort of simple Blues pattern, or even possibly something like Nightclub 2-Step, which would have a sort of "1-a2" count when danced to 12/8 feel.
Regards,
Jonathan