Sony CDP-CX300.
I applied with a Q-tip gun oil (that says it has silicone in it) to the single laser guide rail. That solved my skipping problem. I observed that the CDs always started skipping between 4.18 and 4:54 minutes. That was a clear indicator of a "location problem".
I had previously done some disassembly and cleaned the "rack", then re-lubed it with white lithium grease. This did not work, tho I got a good view of the laser guide rail on the laser assembly that I removed to lube the rack.
To lube the guide rail, I removed the cover, then reached into the access to the guide rail with a Q-tip moderately full of the oil, and wiped the accessible surfaces; the "backside" of the rail opposite the access area could not be reached for lubrication. The access point is located at the rear left of the player when looking from the front, and in between the black plastic. Look for the shiny shaft.
There has been many years since previous posts, but those posts were helpful to me.