Here's how Pierre Attaingnant (ca. 1494-1551/52) did it in his Kyrie (p. 1) from the Mass "Kyrie Fons" (1531).
Of course, this setting is more like hymn verset for three parts rather than a hymn harmonization but the principle is still the same. Here are the steps to follow:
1. Take a hymn harmonization of your choice from any hymnal and practice the soprano part (the hymn tune) one octave lower with the pedals. This will be your new tenor part.
2. Play the alto as written in the right hand part.
3. Play the tenor part one octave higher with the right hand making it your new soprano part (completely different melody will sound in the top voice).
4. Play the bass line of the hymn harmonization with the left hand.
5. Play your new soprano and alto combined.
6. Play the new soprano and the new tenor combined.
7. Play the new soprano and the bass parts together.
8. Play the alto and the new tenor parts together.
9. Play the alto and the bass parts together.
10. Play the new tenor and the bass parts together.
11. Play the new soprano, alto, and the new tenor combined.
12. Play the new soprano, alto, and the bass parts together.
13. Play the new soprano, the new tenor, and the bass parts together.
14. Play the alto, the new tenor, and the bass parts combined.
15. Play the final arrangement of all four parts together.
The good news is that by practicing so systematically you won't feel any pain. Every step will be just a little more difficult than the previous one and you will be amazed at how colorful the step 15 sounds once you're ready.
Play the hymn tune with the Trompette 8' (and 4') and the rest of the parts on the 16' based Principal Chorus with mixtures. If you don't have these stops on your organ, don't worry - take some other 8' stop in the pedals which would sound louder than the manual part.
Are you up to it? If so, go practice and share your experience in the comments.