The relays are rated 20A / 230V (But I wouldn’t go higher than 12A). There also a “snubber” circuit on the PCB to prevent relay sparking and electrical interference noise. They can handle the router without any problems directly.
In my experience, a mechanical relay is more reliable than a cheap SSR. I’ve killed 100A “rated” SSR’s with less than 16A. The annoying thing with SSR’s: when they burn, they keep the contact closed (most of the time). So, if you do want to use SSR’s, buy reliable from a know brand and a trusted source. The cheap Chinese Ebay SSR’s are knockoffs and totally unreliable.