Unless you're really scared by electrosmog, you shouldn't have to worry too much about this. It's a cool buzz word and you can sell protection, counseling, etc. but in the end it's not really problematic, once you look at the bigger picture.
Infrared radiation is essentially just light/heat emitted that you can't see. There's no real harm being exposed to it (in contrast to ultraviolet light/UV). That tiny camera won't emit enough to roast anything. Any artificial light source would most likely emit more UV / IR light and still cause no problems, since the amounts may be ignored compared to natural sunlight.
Similar here, I wouldn't worry too much about it. There's far too less energy involved to cause any measurable harm. Plus it's very likely other WiFi devices of you or your neighbours are causing a lot more "electrosmog" than that one IP camera. In addition, WiFi isn't really powerful compared to wider range technology like mobile phones. Science Blogs.com did the math and in short the energy levels involved are far too low to change or damage DNA no matter the distance. Remember there are even implants like pacemakers utilizing wireless communication and wireless charging. You'd be rather not wise to use something you don't consider safe.
While people can be sensitive to these, power in these lines runs typically at 50 or 60 Hz and as such won't really be able to penetrate anything (including skin) in significant orders. To quote a source, I've googled and found the book Physical and Biological Hazards of the Workplace, page 219, citing home wiring to have an electric field of around 1-10 V/m and a magnetic field of 1-5 mG. Don't worry too much about the units. The important fact here is the natural exposure caused by the Earth itself: 120 V/m and 450 mG. As you can see, the added radiation is typically below 1% of the natural exposure, and as such usually something to ignore (unless you're really sensitive to the frequency).
Besides all that, maybe just offer the pigeon something more comfortable somewhere else, especially if it has problems properly sitting on there?