I really think that you will need the spacer part to do this correctly. Without it, the tractor will run, but the coupler splines will not be fully engaged with the HST shaft splines, and the durability may be reduced.
As a check, when you remove the coupler put it hub down on a table beside the new one (also hub down). If the surface that mounts to the flywheel is is the same height for both, the spacer won't be needed. I am almost positive though that you will find they are different heights and the spacer will be required.