What about level of non ionizing radiation the cat is exposed to? Cats head is always in near field of antenna, seems a bit harsh to the cat.
1. it's a WiFi client , in other words, mostly receiver . 2. even if it were an AP, transmitting at max power for hours, it would give out very limited power (zero, give or take measurement errors). 3. you're starting from assumption "wifi baaaad" without anything to support that claim; if it were a nuclear device, I'd see a cause for concern. [citation-sorely-needed] for this assumption.
Edit: More to the point, it's a good question, even if the answer is "no."