Even 160's will stop you just fine.
I have heard issues with larger disks and fork mounts not designed for such high breaking forces. I don't ride hard enough to care, it's probably just a health n safety don't sue me type warning.
Alligator is a brand name, nothing to do with shape of disk. They make disks in all designs and breaking surface patterns.
Most common now are 6 bolt rotors.
Some newer hubs use a splined centre lock disk.
The mounting of the caliper onto the frame is more than likely IS, International Standard mount. The forks maybe IS or PM, Post Mount.
Adapters are available to fit pretty much any caliper to any mount width and size rotor, eg.
IS - IS +20mm
PM - IS +10mm.
Calipers that bolt directly to the frame or fork mounts are designed for specific diameter disks.
Washers and adapters allow you to change that.
You could mask the braking surface and spray the rotors if you like, they get hot, or so I'm told, if I went faster, shouldn't affect the paint.