Roland Microcubes are awesome for amplifying ukes as they come with built in effects and a range of settings (it's like 7 amps in one + effects)
Perhaps for the money that would cost to fit a decent pickup on your Flea, it may be a better investment to get a good solidbody electric uke.
Such as this Stagg, which is just over $100 (installing a good quality pickup for your Flea may cost even more!)
http://cgi.ebay.com/NEW-STAGG-EUKS-...ltDomain_0&hash=item51933d88df#ht_6232wt_1068
Eleukes and Risa are also quite good (and there are others... there's even a Fluke solidbody electric now lol).
I have always found that solid-body electrics sound better than acoustic-electrics through amps like the Microcube, because you are able to use higher gains without feedback and make better use of the effects and amp sound.
Pickups, if done by a professional who knows what they're doing, will not cause any problems to the instrument.
I suggest taking it to your local musical instrument specialist (generally, guitar specialists can also work on ukes).
Of course there will always be those who oppose pickups altogether and insist that microphones are the way to go... but unfortunately for them, that method won't do you much good with a Microcube lol.
(Well the Microcube can be used with a microphone.. but I'm not sure how successful microphoning a uke on such a small amp would be..).
Active pickups... They're the most invasive, but are the most convenient to plug and play once installed correctly.
They take power (usually battery that only needs replacing once a year or so), and usually have tone and volume knobs built into the preamp.
There's many brands, some popular ones being Fishman, B-band, Shadow... variable prices, but all decent to great quality.
Mi-Si are quite popular and don't take batteries, but you need to recharge them every 16 hours or so (and no tone/volume control).
Active pickups generally cost around $100 and up.
Mahalo have a really cheap active pickup, but the quality is quite poor per my experience.
Don't make the mistake I did - ruin a good uke with a cheap pickup lol. Get a decent pickup
For less modification to the uke itself, there are passive undersaddle pickups. These are generally cheaper than the actives, but are also variable with price/quality.
Good quality undersaddle passives should sound ok through the Microcube. Risa uses Shadow nanoflex passives on their nylon string electrics, and that works well - though there is more feedback hum with them than active pickups. An external pre-amp would do wonders to this though. I think some professionals (including Jake Shimabukuro? Aldrine?) use a Fishman passive pickup..
I think there are many people who prefer this option - getting an undersaddle pickup and output jack installed is only moderately invasive, and the quality of the sound can be adjusted depending on the external pre-amp you use (though the Microcube should be able to handle it directly without the pre-amp if you're not overly fussy about the sound quality).
I guess stick-on pickups and transducers are the minimally invasive.
I'm not a big fan of this type of pickup, because they don't sound good if you connect them directly into an amp..
External pre-amp would be essential in getting a quality sound from them.
For amplifying acoustic ukes on the Microcube, if you're not happy with their default "Acoustic" setting, try turning the gain down low and setting the amp knob to "Mic".