Black trim sounds like DF, white and black fabric would be early production (later would be smaller ports covered by paper). Last indicators would be the color of print on the headband. Silver- DF, gold-Monitor, and on the lids (large plastic ring on the outside ear cup) "Studio Monitor" is printed on the DF, and blank on Monitors. But black trim was only DF, and it seems from what I know, only one driver type was used.
You may want to replace the foam ring under the lid, you can buy them through AKG (phone call), or Full Compass Systems (on-line). It's only about $4 for two. The foam deteriorates and black flecks will fall out the back between the disk lid and housing. It can also eventually get "gummy" and fall into the baffles.
The disk lids can be removed by removing the earpads, then using a thin non-marring tool (think good plastic), insert the tool between the lid and housing and gently pry up on the lid, using the housing as the fulcrum point. You can also slip a piece of thick cloth, thin leather, or rubber between your pry tool and the ornamental ring on the housing. Don't want to mess it up, it's aluminum and will get marked up if not careful. I usually place the headphones over the end of my work table so the side I'm working on sits flat on the table. Don't pry too hard if it's stuck. Just keep steady pressure and use your finger nails to grab the lid where it meets the disk and pull up on the lid at the same time. It should pop off. They can be stubborn if they haven't been opened in 30 to 40 years.
Once loose it can be maneuvered over the headband and out of the way. The left one will need to be maneuvered over the cord as well and the stress relief sleeve will be in the way, but just work it over the sleeve.
Then clean out all the old gunk, and stick in the new foam. Most say the foam has no real sonic impact. The purpose is to keep the housing from bumping into the disk.
You may also want replace the elastic band adjusters (rubber loops). Also available at Full Compass. Unscrew the slider and remove it and it's disk. The rubber loop will probably be stuck to the inner headband. Take note of the orientation of the holes on the rubber loops disc and how they align with the slider. Pop
the rubber loop loose from the headband. Install the new rubber loop to the headband and slider. Now the other end.
Remove the screw holding the housing lid (under where the side plates would normally be), and lift the housing lid off. I'm pretty sure this is when they went to a two screw vs screw in a screw arrangement, so there should be a hole in the center of the housing lid with a screw visible through the hole, and a screw above the hole. Remove the screw above the hole to remove the housing lid. If just one screw is in the center of the housing lid, remove that screw. A larger screw holds the outer headband to the housing (the one seen through the hole, under the housing lid). Remove this screw, pull the outer headband gently away from the housing just enough to pull the rubber loop out. The outer headband is still attached to the cable (left side) or the driver(right side) so be gentle as to not detach the wiring. The rubber loop sits around a round extension on the outer headband plastic mount. Stretch the new loop over the extension, and reinstall the outer headband to the housing. Reinstall the housing lid. Done.
Lots of words, little work.
Attached is the service sheet for reference and parts numbers. Diagram is for modern K240 Studio, so some things are a little different (xlr connector, plates, etc, but should still be useful.
DFs are a unique member of the K240 family, enjoy them.