It won't affect the club.  Many pro's use different grips on their putters anyways.  Jason Dufner uses the Super Stroke grip and does just fine.  I for one, wouldn't go put a cheap standard grip on my Scotty.  If it were a larger than standard grip, I would see no problem with it though.

I think it all comes down to what you prefer. Go with what feels right and gives you the most confidence on the greens.

If i were you, I would try to put a Scotty Cameron grip on, but another brand I would try would either be iomic, or maybe Golf Pride.

I hope this helps

I replaced mine with the same png grip Tiger used on his Scotty and his present swoosh Method- really got  a great feel and texture to it....I guess I wouldnt if it were a putter that was just part of a collectible collection but I use my Scottys so its all about how good the grip feels in my hands...

Rickey Fowler put a super stroke on his scotty cameron putter so its not bad but probably not recomended

Install whatever grip you like on the putter. It doesn't have to be a Cameron to work great on the course. The grip just reflects your personal feel and taste.

you can put any grip on a scotty. i say if you like the scotty grips get a new one but if you dont like it try something esle

Png Man Black Out Putter Grip. 

Try the Scotty Grip that comes on some of the new putters, the Pitolero.  I got it also for my old reliable Red X, love it

I replaced mine with the same png man blackout grip - really got  a great feel and texture to it....I guess I wouldnt if it were a putter that was just part of a collectible collection but I use my Scottys so its all about how good the grip feels in my hands...