And a slightly more ridiculous suggestion: if you have a modchip, you could patch a backup of Brawl to autoboot.
But yeah, if you can't get your hands on a replacement sensor bar soon enough, I think a Classic Controller will control the System Menu (not a GC controller, though).
Or any pair of infrared light sources will do - all the sensor bar is is a set of four infrared LEDs on each side under the shiny black plastic. Candles (as mentioned above) emit IR as well as visible light so they'd work apart from the whole candlewax-on-your-TV thing. You could potentially get away with holding two TV/DVD/etc remotes roughly that far apart with a button held down on each if you were feeling masochistic...
While I'm rambling about sensor bars, a good way to check if your sensor bar is working is to look at it through a digital camera's screen - I think really expensive cameras include IR filters but most don't, so you can see if the LEDs are lit.