This is a relatively easy mod. I deliberately did not touch the motherboard of the microKorg; in fact, you don't even need to remove it. You need to solder 1 wire to the barrel jack PSU socket though. Depending on your skills, this procedure will take about 2 hours: 

• The biggest obstacle lies in finding some decent low-profile speakers that sound good and will fit in the case. They have to be slim. I got a very nice pair of neodymium 20W full-range speakers. They sound great and have a decent punch. I doubt that the microKorg s will sound much better than this! 
• Next, you will need one of these PAM8403 D-class stereo audio amp modules that you can get for 5 $ on eBay. 
• In order to bring the 9V down to the 5V that the PAM module requires, I used a simple 5V regulator. Its heat sink I screwed to one of the loudspeaker's metal casings. This will cool it (I doubt that it will get very hot anyhow). Use two 10 uF electrolitic capactitors with their "-" pins soldered to the middle (GND) terminal of the voltage regulator, and their "+" pins soldered to the left and right regulator terminals, resp. (left = 9 V input from battery compartment or PSU socket on the motherboard, right = 5V output goes into the PAM8403 module). 
• Also, you will need a "double pole double throw ON-ON Guitar amplifier 2 way" switch. This is to turn on/off the PAM8403 amplifier, and to power it from either the battery compartment or the PSU / barrel jack. At first I thought it would suffice to only route wires from either the battery compartment or from the barrel jack to the PAM via the switch, but then the amp is only powered if run either from the battery or by the external PSU, but not both.
• So you will need TWO separate power feeds into the PAM module: one for battery route, one for the PSU route. The switch selects the route or turns it off. That means you need one pair of wires (+, -) that run from the battery compartment to the top row of double pins on that switch. The middle row of double pins go from the switch to the left terminal (9V input) and middle terminal (GND) of the voltage regulator. From there, route the middle terminal to GND off the PAM8403 module, and the right terminal (5V output) to the PAM's 5V input. The last row of double pins on the switch run to the + of the PSU barreljack on the motherboard, and the other one to GND. See the pictures. Be careful not to mix + and - sides. The left colum of pins of the switch has to be -/-/GND  (Battery, PAM, GND from Motherboard), the right colum of pins is +/+/+ (Battery, PAM, Barrel Jack from the Motherboard).

• Note that the amp will drain your batteries if left on. 
• The plastic of the microKorg case bottom is easy to drill - I simply used a Carbon Steel Wood Drilling Bit, Spade Style, 1 inch. Depending on the diameters of your loudspeakers of course.

You will be amazed by how good that sounds! The microKorg case makes a good resonance body. Check it out: