Help needed for wiring Kohler engine swap

[Colimotl]

I have a Cub Cadet tractor SuperLt 1554
Model: 13AK11CK712
Serial: 1D075H30108

and I am in the process of replacing a damaged 27 hp Kohler engine
Model: CV740S
SPEC NO.: CV740-0026
SERIAL NO.: 3508021671

with a new 23 hp Kohler engine
Model KT730 DISPL (CC) 725
SPEC NO. KT730-3012
SERIAL NO. 4409307693

I have everything completed and am ready to hook up the wiring. QUESTION: Can I safely hook up the matching connector from the key switch to the connector from the engine?

I believe that both the 27 hp and the 23 hp engines have a 15 amp alternator.

Below is information concerning the ignition switch:

From the Cub Cadet Service Manual: The Key Switch is similar to those used in a variety of MTD applications since 1999. The difference in this case is that it is incorporated in the same housing as the RMC module; the two items are not available separately.

In the OFF position, continuity can be found
between the M, G, and A1 terminals.

M is connected to the magneto by a yellow wire,
G is connected to ground by a green wire, and
A1 is connected to the after fire solenoid and
alternator.

In the OFF position, the magneto primary windings
are grounded, disabling the ignition system.
The alternator output that normally keeps the
after fire solenoid powered-up is given a more
direct path to ground, depriving the after fire
solenoid of power. This turns-off the fuel supply.

One concern that I have is that when I attempt to connect the molded connector from the ignition switch to the molded connector from the engine, the colors of the wires do not match. See the drawing below:

Any assistance will be greatly appreciated.