If torches don't work, you can always try covering the spawner with a couple layers of blocks, then get rid of it when you're done. If any blazes do come through, you could always finish it off with snowballs and a sword.
blazes can spawn in a light level of either 9 or 11 (I forget which it is, but it's on the wiki). If you want to 100% block the spawns from a blaze cage spawner, it's probably easiest to simply fill in the space with solid blocks or at least glass (mobs can't spawn on glass). You will want to fill in 4 blocks on all sides of the cage, both on the same level as the cage as well as 1 block above it (for good measure, might as well also do 1 block below the cage but there's no room for a blaze to spawn there because of the middle layer).
You could also just surround the spawning cube with fences with a floor of carpet (there's a possibility of blazes fitting through the gap between a 2x2 section of fences).