Electric over hydraulic is expensive, but adding a surge coupler to the tongue wouldn't be too bad. (I see a Titan drum brake surge coupler for $166 on ebay...) It would work fine with the S10 brakes, except that you'd have to pin it to back uphill... Trailer hydraulic drums usually don't work well in reverse, while the S10 drums will likely stop you from backing up if the trailer pushes much on the tongue... FWIW, I have three surge brake trailers. They all stop very smooth, and I don't feel them pushing on the the truck much at all regardless of load.
IMO, as an engineer and fabricator, it would NOT be "easy" to get trailer brake components into an S10 rear axle. And that coming from a guy who underestimates the difficulty and time to do almost anything... They are certainly both drums, but that's about all they have in common... Trailer brakes are very simple, and the drum is also the hub for wheel bearings. IF the S10 happened to have 9" or 10" drums, and you could mount the elctric brake backing plate to the S10 axle in the right place with respect to the drum, it could work, but you'd have to buy electric brake parts, and luck out on drum size, geometry, etc... Plus you have to pull the diff cover to get the c-clips off and pull the axle shafts to remove the brake backing plate and install the trailer plate, if it would even fit, or could be made to, then put it all back together and refill the diff with 90wt... What a mess...
Seriously, spend a little money and buy a complete trailer axle with brakes off Ebay. It'll be lighter, easier to service, and probably just as strong as the complete S-10 axle. You might have to change wheels, since most of the ~3500lb 5-lug axles have a 4.5" pattern, while S10's are 4.75", but older Jeeps and Ranger/Explorers used the 5 on 4.5" pattern, so wheels should be cheap and easy to find. With a trailer axle, you'll have a setup that works just like it should, doesn't take 90wt, and works as soon as it's bolted in. THAT sounds "easy" to me.
Here's a
$225 axle to your width and spring pad specs that includes brakes...