If the true goal is to be an introduction to music, as stated, then I really have to recommend the recorder. (He says while donning flame-proof underwear...)
Melody and rhythm are the first components that should be approached in an introduction to music and that is most easily done with a very simple monophonic (one note at a time) instrument like the recorder. The recorder is also quite inexpensive, even compared to ukes, and requires even less motor-skills than learning C-F-G chords on the ukulele. There are reasons that recorder has usually been the instrument of choice for introducing very young students, especially, to music. I fondly remember my recorder sessions in 1st or 2nd grade and I'm sure they went a long way toward instilling in me a lifelong interest in the making of music, even though I didn't really start doing much about it until my thirties.
You might do a six-week introduction to music on the recorder, then follow it up with a six-to-twelve-week introduction to accompaniment on ukulele where you can begin to introduce the concept of harmony, instrumentation as the foundation for vocals to build on, and so on.
John