Is this OLED LCD the same from the link you link you've sent?
It looks similar. 0.91 inches and a resolution of 128x32. Both show the same SSD number - SSD1306. However, the display you posted seems to be white. Ledger uses a dark one. The first couple of pictures on the link that dkbit98 posted seem dark. The last one is white though.
Pay attention to the pins.
The video description that dkbit98 posted says it has to be 12 pins because the Ledger socket is 12 pins. But the one on
https://www.buydisplay.com/0-91-inch-128x32-oled-display-with-connector-fpc-ssd1306-white-on-black has 15! I don't think it will work. The one you posted doesn't have 12 pins either. I count 14 or 15.
Check out the description link in the YouTube video. There is a link from where you can purchase the correct display with 12 pins.
https://www.youtube.com/watch?v=dSwmk4GW4GIWill there be no issues in terms of security?
They claim to have fixed the vulnerability of OLED displays with one of their old firmware upgrades.