There should be no danger that anyone might think wrongly of fear, depression, or a bad odor. Those senses are all uncommon and old-fashioned (if not indeed obsolete), and in any case they're all normally associated with the noun 'funk,' not the adjective 'funky.' I also agree with ken that I've never heard anyone use 'funky' in the sense of 'lacking style or taste' (M-W sense 3b).
The positive style sense and the musical sense are the only ones really used in modern AE. Based on their connotations, the word 'funky' can indeed be used in advertising, and often is.
But 'funky business' sounds like a deliberate play on 'funny business,' which means tricky or suspicious practices, and 'monkey business,' which means either the same thing or shenanigans, misbehavior, etc. Not associations most businesses want to evoke, unless they market specifically to, say, juvenile delinquents.
It might depend, though, on how you pronounced it. 'FUNK-y business' (one primary accent, one mental concept) would be the same stress pattern as 'funny business' and 'monkey business,' making it sound fishy or shady; 'FUNK-y BUSI-ness' (two equal accents, two separate words) might allow it to sound more unconventional and hip.
Whether it could ever sound unconventional and hip *enough* to overcome the stodgy connotations of the word 'business' itself is another question. For me, pairing 'funky' with 'business' is still something of an oxymoron. (-;