It depends on the patient.
I've refinished a ukulele only once, because it was already refinished but in a bad way, and because it was an instrument of low cost (but high value: fleamarket bargain, which plays well). Lots and lots of sanding, especially in the nooks and crannies, and then choosing a light varnish, applying thin coats and sanding in between them.
With better, more costly ukuleles that had serious scratches or worn-out patches, I've often gone down the path of cleaning, and putting on a thin wax. The wax is removeable, protects the wood but doesn't really affect the sound much because it hardens. Plus it smells good.
I'd avoid oils at all costs, save perhaps lemon oil for a fretboard. It stains, but doesn't protect except through a bit of saturation.
In any case, avoid the hard film 'boat lacquer' PU (polurethane) or acrylic varnishes, they will kill the sound by essentially shrinkwrapping your uke in a thin plastic foil. Rather look for alkyd based ones, or if you go with a wax, the most natural product is bees wax.