Are you using any glitches specific to the SNES one/one of the versions of it (JP 1.0, etc) for the Swordless run?
If not, I'm pretty sure the lamp will open those curtains in the GBA remake (it also does damage when it hits enemies in that version, but your post above showed that might not be too necessary, you managed to get the Bow fine without any way of harming enemies).
I can test this later if you say the glitches work the same in the GBA one.
http://www.youtube.com/watch?v=563xdKTT-AQ
0:55 I recall asking someone from here on YouTube soon after it was made if that specific glitch warp is possible in the GBA one. Unfortunately, he said no, you get stuck in a wall instead of going in Hyrule Castle as the video shows.
I'm not sure how you did the glitch in your video above to get past the guards, though. Multidirectional stuff?