As always, there are no bright lines with regards to "fair use". You could defend your usage based on the balance of the four factors: the amount and substantiality of the portion used in relation to the copyrighted work as a whole is low; the effect of the use upon the potential market for or value of the copyrighted work might be low. In the past, image rights have been licensed for a hefty profit, so there is significant risk in depending on a negligible effect on market argument. A third factor, "nature of work", works against you: copyright is especially designed to protect creative works of art and literature.
While not binding, there are analogous uses where the city of Seattle claims to also be fair use (unless the attorney is just wrong and there's a lawsuit waiting to happen). One difference is that the city additionally claims that their "street art" use is "educational", which is a fair-use friendly "purpose of use" factor (whereas commercial exploitation is anti-fair-use). In this case it is not a heavily commercial use (you're not selling the product), but it has the purpose of increasing your business, which is a commercial use. Finally, the suggested use is rather "transformative", which is a good thing because the more transformative ause is, the less the four factors matter.
It appears that permission to use is granted almost automatically in this case (as long as you register and formally ask) so fair use needn't be your only recourse.
In short, it is not clearly in and not clearly out, which is the situation that calls for an attorney to give professional advice.
