Moved to “Ukulele Q&A” 😉
Hmm, it is indeed difficult to ‘electrify’ your ukulele. Easiest option is to buy an acoustic-electric one from the bat of course 🙂 But I myself have not done so.
Before I’ve learned to play the ukulele, I’ve played the guitar (still do). And I always bought an acoustic version, even if an acoustic-electric one was available. This is because a befriended luthier told me that the internal electrical components interfere with the sound waves with the guitar its body having a negative on the output of the sound. If amplification was necessary he would always suggest a (passive) sound hole pickup which you can simply install in the soundhole when required and remove afterwards. This advice was given to me several years ago (around 2007) and till today I still keep it in mind. I have used many soundhole pickups and found that generally you get a lot of bang for your buck. There are some very inexpensive models which do the job perfectly. I must confess that I currently own a Taylor guitar with an extremely decent ‘expression system’ to amplify the sound.
TL;DR I’d suggest a soundhole pickup, like for example this one (which also looks the part): https://www.musicianswebstore.com/proddetail.asp?prod=SH330&cat=1590
Hopefully this helped you a little bit 🙂