So don't have the bike here to check, why won't a deep socket and normal ratchet work??
Because ideally you need to hold the centre screw in position at a quarter turn out whilst tightening the locking nut on the outside of it.
From memory the locking nut is about an inch inside the sprocket cover housing, hence the need for the offset ring spanner.
You can bodge it, by just hoping the centre screw stays put if you tighten the lock nut up with a socket, but there's a high chance it will move, creating gear changing problems.
That's why i'll always ask if someone has adjusted their clutch at the lower end if they ever have gear problems 'cos chances are it can be corrected with that centre screw.
If you're gonna put a shiny new cable on your bike then do things right from the off.
And lube those bearings too, that makes things feel even better.