It looks like those are cartridge bearings, they have a couple of lock nuts over them. At least that is how it is on both my fixies and they look the same as the one on the left. The one on the right could be cone.
I needed to do this as well when I was building the hack fixie.
Rest the axle end up on the flanges supported by a few layers of cloth so you don't scratch them and gently tap the end of the axle, the bearings on the bottom will come out. Turn over and repeat.
You will notice that the axle is not threaded for the length, but contains smooth bits and flanges for seating the bearings. Try to find a longer axle with the same internal dimesions, just longer threaded ends.
Putting the bearings back on is best done by loosly fitting and then gently tightening the lock nuts to bring it all together.