I never owned a Kindle 4 so can't really tell if and what built-in font family was available on that firmware brach used by Kindle 4 and are not?? also available on firmware 5.x.y? Non-condensed version of Caecilia?
Also, IIRC Kindle 4 doesn't? use firmware updates that are complete filesystem images like newer Kindles but instead uses patching / replacing only changed files similar to Kindle 3 / Kindle Keyboards?
And that fact probably plays a role in how one needs to approach extracting the font files.
What exact font family do you want to continue using on Kindle Oasis?
edit: Just checked and yeah, Kindle 4 uses "patching" approach to firmware updates so the font files can't be just extracted from update bin like they can with firmware 5.x.y used by newer Kindle models.
Soo, in order to do that you will need to jailbreak your Kindle for and get to font files via SSH / USBNetworking hack... or check if
Fonts hack for firmware 4.x also has and option to backup all built-in font files like it does for firmware 5.x.
Or ask someone here that also has Kindle 4 that is already jailbreak-ed to do that for you and send you the files
via PM.