So I just found a stronghold and located the End Portal. I tried lighting up the area to get rid of the silverfish that come from the spawner, but I found out trough the Minecraft Wiki that when there's a spawner they can spawn at any light level.
Since I don't want to destroy the spawner, is there any way I can disable it? I know I can fill the room with blocks, but then access to the portal would get quite a bit complicated.