I've done a fair bit of amateur recording Phil and I just want to echo what William said...try it out and experiment with it for yourself, but my experience is that when you're only recording on one track in a single take, the important thing is to get that mic much closer to your voice, as it *should* pick up the volume of the uke no probs (with a guitar you'd need to be even closer)...but just play around with the distances and work out where the optimum position is for the particular mic you're using.
That said, a $30 mic will sound like a $30 mic pretty much. The goal probably would be to save up and get yourself a nicer one up closer in the $200-500 zone, then you will really notice an incredible difference...to the point you'll sound so good you'll wonder why you're not being paid for your work!!!
Mic quality is such a huge deal. I have an old mic I used to use with my tascam 4-track and it is junk. I also have one that cost me $450 and the difference is beyond comparison. For yootoob clips I just use a $99 hand held Fuji JX3870 camera which is good enough for what I'm after. But with all that said, your first recording sounded REALLY GOOD man, I'm really surprised you got it so cheap. Well done brother.