I accidentally trashed my Oblivion Game of the Year disc, and I'm able to buy a new regular Oblivion disc.

Will I still be able to install + play the expansion content (Knights of the Nine + Isles) using a regular Oblivion disc instead of the GOTY edition?

Well unless its GOTY you can only play regular oblivion. Or, you can buy the regular oblivion plus the shivering isles expansion pack. But its just easier getting GOTY.