On the same trellis you can't realistically prune them differently. You can hard prune both of them, and the Henryi will bloom a bit later than if you hadn't hard pruned it; mother nature often hard prunes my type 2 prune plants down to the snow line or even the ground, and they grow and bloom just fine. Then the Jackmanii will bloom after that.

In a 1/2 wine barrel I have Henryi (2)and Roguchi(3). So far-they have been together for 3 years. The Roguchi does not tend to cling like Jackmanii and Henryi but grows straight up supporting itself here and there but still it is a challenge to prune them. If your trellis is wide perhaps it will work for you if you plant them far apart and let them twine further up so that you have more control when pruning. My two become a mess of tangled vines at soil level....

Vanessa just prune them both like a type III and don't worry about shading the roots. They need to be evenly moist not shaded. Using mulch better than competing groundcovers