Well, I am not entirely sure how the Egyptian sun god is meant to be pronounced, but I pronounce it in the same way as I pronounce "yahoo". It is similar to "car" (but without the "r" sound of course) or "fa" in tonic sol-fa musical notation. OED gives the IPA pronunciation /ˈjɑːhuː/
However, I see that dictionaries give widely varying pronunciations. Collins (BrE) in
yahoo - WordReference.com Dictionary of English has /jəˈhuː/, shifting the stress to the second syllable and reducing the first syllable to a schwa, while Random House (AmE) on the same page has a different pronunciation with the second syllable stressed: /yɑˈhu/. Both OED and Random House have an AmE alternative of /ˈjeɪˌhu/
I don't think Swift provided any clue as to the correct pronunciation of "Yahoo", and certainly the word "Houyhnhnm" (the name of the race of intelligent horses living on the same island as the Yahoos) has given many readers great problems with pronunciation.
By the way, I remember it being used in a DuckTales episode once, so it can't be that outdated.
Made in 1987-1990 according to Wikipedia, so that predates the internet company (founded 1994).