Don’t use any of the old type mains driven fairy lights, they apart from anything else are really dangerous. Think about it loads of bulbs connected to the mains in series to soak up the voltage with no isolation, MADNESS!!! My Father years ago was changing a bulb and because the potential between each holder and earth is still 230 volts here in the UK, he got a very nasty belt from the holder that came loose from the plastic flower shaped thing.
Wow, we didn’t need fairy lights after that, the air air was blue and red for a while because of the stream of foul language coming out of my old man’s mouth! Oooo, I never heard words like that before then.
there are so many low voltage LED light sets around these days and they are cheap. Throw away the old mains ones and stay safe, have as many multiple colours as you like chasing, blinking and any random pattern you can think of all without upsetting your router signal.
Please avoid the very cheap market and dubious on line places as the PSU’s can catch fire. Or if you insist on using your old mains set, bypass the flasher and blink your eyes every second.