It is most likely not a wireless router. The frequency range is so different that it is highly unlikely that a router is causing this. Ham Radio, or an over modulated CB radio is more likely to cause these symptoms, but there can be other interference sources as well.

If you have the option to use A/V connections, it would be much better than the coaxial cable, as even without the interference issue, the coaxial cable connection option automatically makes the picture noisier. Most routers are on 24/7, so you would most likely see it all the time if it was a router.

You may have a leaking cable TV connection somewhere in your building that would be more likely to cause this type of interference. This sounds like some type of radio frequency interference that the TV itself is picking up, and it is not coming from the converter box itself, but is close by to the TV location and is getting into the RF receiver section of the TV itself.