I have this horn that works great, but looks terrible. Before I get too carried away, it looks like I have to drill out the rivets to disassemble it for sandblasting. Is this correct?
I would. You don't want to get sand in between the pieces. I have never seen one riveted like that. Just screws. You may not want to sandblast the diaphram as it might affect the spring steel.
Just my opinions.
I'd leave it alone. Especially if it works. Stick some newspaper or rags down the horn so you can blast inside it a bit (what you can see if you look down it for some reason). Tape off the rest and go at it. No body i'll know or care what's 3 " down the horn as long as it looks good & beeps.