Here's a quick set of ideas:

On a surface mimicking the interior of your kayak at the location of the future skeg, glue (polyvinyl) a 14" x 4 1/2" tall pc of 1/2" foamcore along the narrow long edge. Lightly spray w/ sprayglue and apply a layer of saran wrap 2" around the surface just touching the bottom of the foamcore. Stick a 2" long pc of 1/8" in. dowel into the 1/2" x 4 1/2" edge of the fcore at 1/2" down from the top so it sticks out 3/4". Do the same thing 3 1/2" down (1/2" from the bottom). Starting 1" away from the foamcore, lay out some 6oz cloth (no epoxy yet) and immediately cover this flat area w/ tape (duct or masking). Do same all around. Now that the edge is all protected, fold back the cloth over the foamcore and build the box making sure to cover the dowels somewhat. Add some layers. Let set up.

Next day rip the box off the surface, dig out the foamcore, and throw in a bucket of hot water to get rid of the paper. (You maybe could have glued the flange down w/ white glue before). Drill out the dowels w/ an 1/16" drill.( I guess you could have used 3/32 dowels).

You now have a skeg box, with an unepoxied flange on the bottom, and two nipples out one end - one up high and the other down low.

Now for the skeg: this could be varied greatly so I'll use simple materials in order to explain it easier. I'm leaving out wood protection steps for brevity.

Cut a 4" circle out of 1/8" aircraft plywood. Drill ctr for 5/8". Cut two rectangle of 1/8" ply at 4" x 13". Drill 5/8" hole 2" from end in both. Sandwich all 3, and glue together. Shape to form a skeg!

Take 15' of 1/16" aircraft cable and thread half thru the little opening around the circular cutout in the skeg. Attach the cable to the skeg 2" back from the front(as if the skeg were retracted). I'm not sure quite what to use but a round topped s.s. screw thru the middle of the strands might be fine. Now drill a hole thru the skeg box at the corresponding skeg location leaving 1/4" clearance all around. Push skeg in place and provide an axle similar to the approach used by others here for end grab rope holes. Thread cable thru nipples.

Now hack your yak. Cut the slot, glass in the flange from below.(could also mount from i/s - modify dims). Jam 1/4" or 3/16" surgical rubber 5" long over the nipples. Clamp in place (heat shrink?). Heat shrink the other end over the ss. a/c cables (the idea is to get a good friction fit). Extend cables thru your cockpit to somewhere around your toe or heel locations. Attach to some tiny pedal or swing. The idea is that one foot deploys while the other retracts!

Please note: -- this is just at the spur of this moment - I haven't done it - yet!