Dug deep into my memories of the turn of the century for this one. Yes, I was living in Ichikawa and there were a number of songs that had their time in the spotlight for a while before disappearing into the pages of a karaoke guide book only to be later re-discovered by some pleasantly surprised amateur singers.
Case in point: one of those songs is "Aah, Yokatta" by Hana*Hana（花*花）. Hyogo Prefecture's Izumi Kojima and Makiko Ono（こじまいづみ・おのまきこ）, who have known each other since elementary school, formed the duo in 1998, and they had their indies period in which they released 6 singles between 1998 and 1999. That 5th single was "Aah, Yokatta" which went as high as No. 91 on Oricon.
Once they got their major label, though, Hana*Hana decided to debut with "Aah, Yokatta" with the added "Setagaya Mix" in July 2000. I don't know what the original version sounded like so I can't make comparisons but the "Setagaya Mix" sounds plenty happy with that slow strutting beat. I can even hear a bit of Motown in there.
As for the translation of the title, there are a number of ways that "Aah, Yokatta" could be expressed such as "Oh, What A Relief" or "Oh, What A Stroke of Luck" or "Oh, I'm So Happy". But considering that the lyrics and melody by main vocalist Kojima are about how happy she is that her significant other has been by her side through thick and thin, I would probably go with that last option. Certainly, I think "Aah, Yokatta" would be one of those songs that would be played at a Japanese wedding reception.
The really modest showing on Oricon for the original version wasn't copied by the "Setagaya Mix". In fact, it broke into the Top 10 by peaking at No. 5, selling over half a million copies. In addition, it also ended the year by finishing as the 57th-ranked single, plus the duo received that invitation from NHK to the year-end Kohaku Utagassen in 2000.