9-spd and greater chains are more narrow than 3/32 and will not fit on many 3/32 SS cogs which do better with a 5/6/7 speed 3/32 width. I have issues with some 6/7/8 spd chains with 7.1mm outer plate width. The inner plates are even more narrow and this doesn't provide adequate clearance for chain to seat properly onto the cog. The SS cogs tend to be considerably thicker than a multi-spd FW sprocket thickness since all the wear is going to be on one sprocket and not distributed over a cluster. The only way to know is hold the SS sproket up against the chain and see if it seats with no effort around sprocket and the links of the chain actually touch and rest in the wells between sprocket teeth. A 6/7/8 speed 7.4mm or greater width chain should still be fine with a 9spd compatible chainring.