Since that venerable answer on the mailing list, linked by @romainl, we have setreg('a', []) that clears the register.
Thus, the code could become:
let regs=split('abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789/-"', '\zs')
for r in regs
call setreg(r, [])
endfor