Hawthorns are usually pruned once after the first flush has hardened off. Then again after summer to remove any extensions. The first cutback usually yields a good deal of bud back. Ours will backbud on old wood at the node…. and sometimes at other places.
That said, the best way to develop these are a little wire and a good deal of clip and grow. However in this specific case it looks like the best way to proceed is wired sacrifice branches with 1-2 x year cutback as indicated by the tree‘s growth patterns.
Cheers
DSD sends