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The hole thru the shaft inside the steering box is smaller than the hole thru the steering column.
When installing the new horn wire from the top it will most likely be caught at that joint unless guided by a small pull wire or string that you connect to the old horn wire when you remove it.
Fasten the bottom end of the new horn wire to the pull wire / string and give it a wrap of tape to help guide the new end into the hole thru the steering box shaft. Keeping that wrapped joint small will be important.
Using a long piece of wire with a matching bullet style connector as the 'pull wire' may be an even better solution.
Disclaimer: I haven't tried reinstalling a horn wire yet, only recently removed one to remove the steering column.