Referring back to the OP. We have a person who has some musical experience in a single note wind instrument looking to progress on a ukulele.
This is just one of several approaches that can build on your current knowledge and experience. One thing that will help a lot no matter what you do is finding some ukulele calisthenics, you do the exercises to grow your muscles not your music so don't worry what they sound like.
Learning the ukulele is a good opportunity to change from a focus on the melody part to the rhythm chordal part of the music. If you adopt this as an overall goal, to go along with using the ukulele for musical relaxation, you can give yourself a focus to look ahead to see where you could go. So maybe read a book about rhythm and percussion, use your uke as a musical drum to play the exercises in chords.
Other things you could try.
Just follow the usual path of learning a C chord and working up to more chords, following tunes learned from videos or in a group. This is the path to musical recreation and relaxation, but it may not be much of a musical challenge.
Or you could use a fretboard map to work out scales, I would start with Db major starting on first fret of C string, and the scale pattern on the fret board. Move along to Eb which starts at the 3rd fret, then F at the fifth fret etc.. The pattern repeats all along the fretboard. You already must know some single note melodies from the wind instrument, so after learning where the scales are, noodle out the melodies you know by ear or from reading, it makes no difference. Then as you get smooth with single notes, add in the thirds using two fretting fingers, then add in the fifth with three fretting fingers, then add a colour note like a 7th, 6th, 8th, 9th, b5 etc. with your fourth finger. Arpeggiate or strum, it makes no difference while you are getting started. You will end up playing a chord melody. Then bury the melody in between a bass note (low 6th?) and treble note (3rd). This takes four lines to write and maybe two years work to achieve.
Or if you enjoy classical music, find some music which has notes from C D E F G A B c d e f g a (I have left out # and b). This is the range of notes on your ukulele. You can arrange any music with these notes on your ukulele. Or there are some books which have the music arranged for you.
Or if you like another genre, find a music book or video from the genre and transpose the music into the range shown above and just play it straight from the book or video, starting very simple with a (sung?) single note melody and a very simple strum pattern. As you get to know the tune more, improve the strum pattern and chords.
A thing to remember with a string instrument compared to the wind instrument, apart from a chordal approach, is that you can always use your second instrument, your voice to accompany your playing, and you can do exercises to develop your voice when you get bored with ukulele practice.