Your new column has a button (at about 1 o'clock in your pic) for the horn contact. But the old wheel also has a button and used a contact ring on the column.

Just a suggestion but you might be able to glue a brass ring on the back side of the wheel that will make contact with the button on the new column. That ring would have to also have contact with the button in the old steering wheel and be isolated from ground. The horn cover on the old wheel would make contact with the button on the old wheel and the column shaft to ground the circuit.

I see in your second picture that there's a piece with a brass ring. If that fits below the wheel, then you could thread the wire attached to it thru a hole in the wheel and connect it to the plate that goes under the horn cover. That piece with the brass ring would have to rotate with the wheel.

Kevin
1951 Chevy 3100 work truck
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1929 Ford pickup restored from the ground up. | 1929 Ford Special Coupe (First car)
Busting rust since the mid-60's
If you're smart enough to take it apart, you darn well better be smart enough to put it back together.