You would need the part number for an effective search on something like that. Though blower style fans are usually all a standard part, I doubt they went full custom on it. Worth an email to the manufacturer.
Silicone oil may not be an ideal lubricant for the fan. Adding such things are usually stop gap measures before fan failure. Also, depending on the bearing type, it could be harmful.
Oscillations are inherent in anything with moving parts. No machined surface is truly perfect, and this is far from precision work. These things aren't designed to last. You say the problem only occurs at certain speeds, that says that some harmonic or sympathetic vibration is happening with something. Could just be a small defect on a ball bearing or surface, and at that revolution it pushes it in just the right direction to set up a reinforcement in that direction every time it comes around. Coupled with some minor imbalance in the fan, it would cause an oscillation that gets amplified every revolution.
Hmm, I would want to take apart the cooler to see if it actually uses ball bearings, but it might:
https://www.ebay.com/itm/For-Galax-...tem4442e99a58:g:LaIAAOSwI~FdSphX&entryapp=dlp
Could be a worthwhile solution. Truly a shame if they used subpar bearings that are susceptible to rusting of all things.