very few type C sprockets come with a "key".. reason is simple:
that's the first thing to shear in case of a failure.. akeystock is easier to replace..
also it's easier to broach a keyway than to "not drill a key"
And no, you cannot just add washer to a B Type sprocket, the collar is too thick, you need to shave it down on one side then add a single matching spacer on the other side to make it a good C Type replacement.
Okay.. we turn in circles...
IF the earth were flat we would be accelerating up with roughly 9.81m/s...
fact is, it's not, and as long you don't know what the actual ratio of your diff is, everything else is pointless I'm afraid
So, go measure it!!
Lift the left rear wheel (right still on the floor or LOCKED)
remove the chain,
turn the wheel until the valve is on the very bottom!
Now strap something heavy to the wheel (make sure it fits between wheel and floor)
turn the wheel slightly and let go...
when it stops swinging back and forth
call that ZERO!
NOW, mark one tooth of the sprocket and make a matching mark
on the frame or diff housing. (make it bright and clearly visible)
slowly turn the wheel exactly ONE rotation
(carefull the weight wants to take over after 180°

)
count the full rotations of the sprocket, when you're conviced the wheel made a full rotation let go and count the remainder (offset teeth in regards to your marking)
let us know what number you came up with
'sid