Lots of suggestions here, but none address the issue that the ADI-21 or any similar preamp is STILL not going to output a signal with enough voltage to drive the line-level inputs like the CD or AUX input.
The simplest and cheapest way to do this, i.e., get the right voltage (about 1 volt to drive line level, AND also get the IMPEDANCE close - about 10k oHms for line leve) is to use a headphone amp, like one of these, and it also gives you a level control as well as a tone control (and is like a stereo out, but actually dual-mono).
This is the BASS version and will sound BETTER than the GUITAR version for UKULELE, for a variety of reasons:
http://www.sweetwater.com/store/detail/amPlugBassG2
He is a cheaper version from MONOPRICE, which I have an also works well:
https://www.monoprice.com/product?p_id=611510
Using EITHER of these, you can use the SAME cable you already have, without the need for the 1/8"-to-1/4" adapter, since these headphone amps have the 1/4" plug that goes into your uke, and their output is an 1/8" headphone plug. I would not consider using this on a stage performance, but if you are careful with it, it should work fine.
Monoprice has a coupon code for 15% off right now 'EARLYBF', which makes it even cheaper.
If you dont want to go this route and have a little bit of a budget, another option to consider might be to use an inexpensive MIXER with a guitar-level input (~$50 for a Behringer), and might ALSO need to use a preamp like the ADI-21 ($29) to feed one of the mic channels of the mixer if it does not have a guitar/instrument input. The you run the MAIN OUT of the mixer INTO the CD or AUX input of your Yamaha amplifier. Then add possibly another $20 for longer cables unless you plan to sit on the floor right in front of the Yamaha.
The mixer will also let you plug in a mic and other things too depending upon what inputs it has.
However, I caution you that anything above a low volume level is likely to fry the piezo elements of the tweeter components inside your nice Infinity speakers.....primarily due to the percussive sound coming out of the uke and how it will drive the physical excursion of both the tweeter and woofer elements inside your speaker cabinet.
A better solution might be to visit your local music shop, goodwill, thrift store or pawn shop and see if they have a used practice amp for like $50, with at least an 8" or 10" speaker in it. 10 watts is enough to jam out in your room without bugging the neighbors, 15 watts will be louder but more than 15 watts is likely going to anger anyone that lives with you or next door to you.
Several smaller music shops in my area usually have a nice stock of Fender, Marshall and Line-6 small practice amps, that depending upon condition start at about $35....if you go this ROUTE, then call ahead and BRING YOUR UKULELE to test it out with each amp and see which sounds best to you. Some of the small Fender amps have reverb built-in, and the Line-6 Viper amps even have modeling and all kinds of effects.
The main thing to ask yourself is 'what are your intentions?' What is your budget?
If it were me, I'd get a real amp and not mess with possibly damaging the stereo speakers, as they were not meant to take the abuse from being driven directly by a musical instrument with a wide dynamic range.
Everything you hear on the radio, vinyl, tape and CD's is 'mastered' and has heavy compression applied so that the maximum volume peak is limited to about -2db so as not to distort and damage your speakers when played at a nominal volume, using something else to drive the same speakers without a brick-wall limiter or 10-to-1 compression ratio is likely to cause damage.
Yep, personal experience - when I was 12 I plugged my electric guitar into the 'mic inputs' on the Sansui tape deck of my parents stereo, set it in record-pause mode and CRANKED up the record input level to ELEVENTY and watched one of the nice $$$$ Bang & Olufson speakers dance itself off the mantel, crash to the floor, breaking the nice wooden box into 4 pieces, while also shredding the tweeter element in the other speaker. Since I was a total Radio Shack nerdy kid back then, I knew just how to fix it all, but I will still chastised and punished. DONT DO WHAT I DID WHEN I WAS 12 (I'm 47 now LOL)
Proceed with caution and at your own risk.
Hope this helps!