Mike,
In regards to the back and sides and their effect on sound. If you have access to an acoustic instrument I have several tests that will answer your questions pretty quick.
1. Strum the guitar while simultaneously lightly touching the back or side of the guitar with your little finger. Do you feel any vibration from the back or side?
2. Place the back of the guitar on a pillow and strum it again. Is the sound or brightness of the guitar diminished in any way?
3. Do the same as above with a pillow on top of a side and ask the same question.
If you answer is yes to any of these questions, the answer if bottoms or sides have effect on the sound should be obvious. Although the sides and bottoms do not have as much of an impact on the sounds as the top, they can and will impact the volume, tone, resonance, and sustain. The tops are designed to work as a head on a drum and to transmit as much volume as they can. Many old world instrument makers were not as concerned with the look of a musical instrument as much as the sound. An obvious example is a Stradivarius violin. They would chose a wood type that gave a desired tone and volume for the top. Then they would pick wood that would fine tune the resonance and sustain for the back and sides and even necks.
Although these points are moot if you just want to have a uke that you can be happy plinking along with like a plastic guitar center special (that sounds ok). It seems obvious that you wish to impart a lovely look to your instruments (something that all of us wood workers love) go with oak. But if tone is as important to you I would use as little oak as I could get away with. Now as I mentioned many times, these are just my opinions they may be correct or not in your case. But I have wasted a lot of fine wood on sad projects by just going for looks.
I'll hop off the soap box now..... Best of luck with you projects. I very much desire to see and hear your completed ukes and to be proven completely wrong.
P.S. If you use oak for the back or sides, Consider building the body a bit larger than standard. The added volume of air inside will help with the sound volume issues.
L.D.