It does not seem possible to register a sim for the busker career unless they have a skill level in guitar. My sims that play drums, bass, or piano would like to be buskers, too.

Inbetween, if you have Mastercontroller, you can simply give your sim the level you want
Sim -> Advanced -> Skill Level
Allows the user to change the level of any skill for a sim
You need Module: MasterController Cheats

Thanks. I actually ended up using MC to give my sims the job I wanted them to have in the first place. I actually have them in a band and the ability to register for the band career is broken. I just gave them all that career through MC, but I suspect I could have given them the busker career directly though MC, too.