Now that you've had your first strumming exercise, let's take a moment to let that all settle in, and to consider a question that may have occured to you as you worked on strumming with your naked, tender finger: Can you use a pick on a ukulele?
There are a number of perfectly legitimate answers to that question, and I will outline them here:
1) Sure. And you can use a pick on a violin, too.
2) Sure. And you can learn to play the piano with your feet, too.
3) Sure. And you can learn to play the vibes with bananas, too.
While there do exist "felt" picks for playing ukulele - that doesn't really count. That may be nice to add an interesting texture to one or two songs in your repetoire, but you aren't really learning to play the uke, if you're learning to strum it with some exotic plectrum.
And I did see a guy play the vibes with bananas once on Letterman. It was pretty cool, but obviously he knew how to play them the traditional way, as well.
Now that we've had a little breather from our exercises, and discounted the notion of using a prosthetic on the strings, let's move on to our second strumming exercise.