This is a subject that comes up now and then, and to answer your question, of the 160 fretted instruments and hundreds of flutes I have built, I have never built any of them without power tools. I am not sure what about using only hand tools would make the process more meaningful. For example, you could thickness your top and back plates using a hand plane, scraper and sand paper. If you get the wood from a lutherie supplier it will be 5/32 to 3/16" thick, and will take you a number of hours. You will learn about grain runout, that really sharp tools are a must and probably get sore hands and arms. Compare that to the twenty minutes it takes me to do the same thing using a band saw and belt sander. Also, if you don't have a hand plane, a good one will be expensive. On the other hand, bending sides over a hot pipe and propane torch is a very satisfying experince. So to really answer your question, you have to examine your motivation. If you only have hand tools and really want to build a uke, by all means go for it. But if you have access and know how to use them, the power tools make life much easier and generally contribute to a better finished product. Anyway, that is my two cents worth.
Brad