I built a quick, fret-less ukulele over X-mas 2012. Sounded horrible at first, in substantial part because of my technique, although there was more to it. Lowered the action substantially. Moved to tuning a semi-tone below ADF#A with GCEA strings, and now it's much better behaved. Fret-less ukuleles have the disadvantage that the only fret is the bone in your fretting finger, which is not narrow, and which is covered with flesh. This causes energy introduced by plucking to be lost to your fingers. You can partially compensate, when possible, by keeping on your fingertips (or fingernails) when fretting, unless you have to barre a fret, which can be problematic in terms of tone. I suspect that you could overcome some of the disadvantages of fleshy, finger-frets, by using higher tension strings, or moving your tuning up a tad for more tension. The higher tension option would be most easily achieved via Aquila's Nylgut strings, if you don't like plain metal strings, or can't do the math to provide yourself with a set of plain steel strings providing the proper tuning and tension. Another possibility is to develop a "lap ukulele" option, because the plastic side of my electronic tuner works very well as a slide steel.
You can, with a few days of time to allow for those moments when you simply run out of patience, or other needs take precedence, manufacture your own fret-less ukulele. Use a plain, round cookie tin, a suitable piece of oak, maple, or poplar for the neck (which is also your fingerboard), four friction pegs, and a little piece of maple molding to use to make a floating, biscuit style bridge and nut. Put a rectangular hole in the side of the tin, near the bottom (opposite the lid), and slide the neck piece through, close to the bottom (on which your biscuit bridge will freely rest beneath the tension of the strings). (How close the neck is to the bottom will control the action at the bridge, which must be very low or you won't like to play the instrument.) You can slit a piece of rubber tubing with a fine diameter and slide it over the sharp edge of the hole, once you're sure you can slide the neck all the way through to the back with the rubber protector in place, to protect yourself, or make up for any gaps. The rubber tubing should flex enough to hold the neck in place. Make it permanent (the tubing) with some gorilla glue once you've got it right. From that point on, you need to find a way to connect the strings at the back, and reverse install a set of friction pegs at the other end. Drill holes into the neck just above where the nut will go for the strings to go through to the back. It's not that hard if you have some basic planning and carpentry skills. I'm sure you can figure out how to use a sharpie marker to add fret marks and dot marks, and how to finish it smooth with Polycrylic once the fret marks are very, very dry. (Make sure everything the strings touch is nice and smooth through the diligent application of some very fine sandpaper and a round file. Steward-MacDonald has a calculator for fret positions and bridge placement, which you can mark.)
When you're done, you can claim to have a fret-less, resonator ukulele!
Fret-less, to me, is a great deal more fun than fretted. It's faster, requires less thought, encourages practice because it's more fun with very low action higher on the fingerboard, and if you can't manage to put thicker fingers in the precise positions needed around the twelfth fret, where the frets would be half an inch apart on a fretted soprano instrument, you can still come up with a reasonable approximation without repeatedly stalling to attempt the perfect landing on the frets while practicing. I remain curious about the lap ukulele option, which I've never played beyond toying around with the electronic tuner's edge on this fret-less instrument, because a fret-less instrument seems ideally suited.
Finally, get used to playing an instrument that won't sound like a fretted, wooden ukulele. If you take it that seriously, then this isn't for you.
Good luck!
P.S. Don't forget to paint palm trees, parrots, or a sunset on the side of the cookie tins to cover up the scratches due to construction! If you're going tacky, go all the way! (Cover the dried image with some Polycrylic for protection when your masterpiece is done!)