Indeed: 1 W is the legal _maximum_ as per FCC rules, part 15. Not even all APs are broadcasting at this power level, this is a WiFi client (meaning that it's only transmitting a few milliseconds out of a second), and this is several orders of magnitude below the power levels used by microwaves. In other words, it is "nothing" for the purpose of cooking your cat's brain.
This would be "guilt by association: microwave ovens will cook your brains if inserted, therefore anything else using microwaves will, too, no matter what the power."
Edit: I see that you didn't mean the question rhetorically - so yes, while this may be a valid concern in the design phase, the total exposure is infinitesimal, even in prolonged use.