This is a design drawing from Zed-Parts website of the mechanical seal. You can see the bellows that seals the carbon face to the metallic housing that gets pressed in to the aluminum seal housing. This really is a complicated way of sealing the stationary seal face (the carbon face) to the housing. Instead of a stationary face with an oring between the outer diameter and the housing, in this design there is 4 seals that have to work in order to seal the stationary face to the cylinder block. There's the seal between the metal ring of the stationary seal, both ends of the elastomer bellows and the oring between the seal housing and the cylinder block. There's also the seal between the rotating face and the impeller and finally the seal across the seal faces. So in total there are 6 possible failure points in this seal design.
In most mechanical seals the spring loaded carbon face is the rotating element and the ceramic or silicone carbide face is the stationary element. The carbon face is built in to a cartridge that's fixed to the rotating shaft and the stationary face is mounted in the pump housing. so in a standard design ther's only 3 seals to possibly leak. An oring between the rotating seal face and the shaft. An oring between the stationary seal face and the pump housing and finally the seal faces themselves.
Do I think it's ok to replace the seal without removing the metal cup of the stationary seal from the seal housing? No. You would be taking a chance damaging the seal between the metal cup and the bellows and not a good idea in my mind.
I've replaced my mechanical seal twice now in 25 years, the first time 15 years ago, not because it was leaking but as a matter of course because the oil seal behind it was leaking, emitting oil from the waterpump weep hole. That was a genuine Kawasaki part I fitted. When I went to recommission the bike last year after a 5 year lay up I found the mechanical seal to be leaking (emitting coolant from the waterpump weep hole). On inspection of the removed mechanical seal I couldn't detect any discernible wear on the ceramic or rubber rotating contact faces. BUT ...I found that the rubber bellows had become detached from it's rear housing (it's bonded in) ...that is the point of failure on these I think. No longer available from Kawasaki, so a pattern one went back in. There were some slight differences (slightly narrower rotating contact face) so time will tell.