Normally a uke or any stringed instrument shouldn't recieve polish more than once a year ( if even that!). Polishes lubricate and moisturize wood which is good but they also clog up the pores and openings in the wood which will cause the wood to loose it's vibrance/ sound carrying qualities. Just use a polish once a year and between that use a dry cloth to wipe it down between sessions. Use a damp cloth to clean messes left by little sticky fingers. I've been using Pledge furniture polish as my once a year cleaner. I spray in on a cloth and wipe my uke down with the strings removed, getting around the bridge real good.
It may be tempting to polish your uke but the wood should really be dry, light and vibrant.
Do lubricate a fretboard more often as this part is under heavy use and bad oils from fingers and sweat salt can accumulate.
An older instrument could stand a light cleaning with a polish but then go back into the once a year routine. Use a cotton ear swab to detail around the bridge, fretboard, and nut. Use a couple of ear swabs soaked with light oil to clean around the tuning rears if you can. You 'll be suprised at the gunk you clean out of them.
Ernest