Hancock works with Ray Embrey to better his image and become a respected superhero (just likein the movie). However, in this crossover, they are not just doing this for Hancock's sake, but to also make superheroes look good again, especially when it comes to the corruption of Vought and the Seven. It can show that superheroes don't need to be associated with anybody to be good superheroes.
I can definitely see Hancock being allies with the Boys. Hancock would be one of the first heroes they actually like or respect.
Given their ambition to create Supes, Vought International and The Seven would no doubt target Hancock and Mary, especially if its found out that both of them are not Supes created by Compound V, but ancient godlike beings. That would definitely put a huge target on their head. Speaking of which, I can see Mary having chemistry with both Starlight and Maieve.
Hancock meeting the Seven is a must. I have no doubt they would want Hancock to join him, but he would flatly refuse. Hancock would definitely have some beef with Stormfront for her racism and Homelander for his superiority complex, especially considering his own origin. Black Noir would be too mysterious for his liking. If Hancock throws that beached whale like he did in the movie, that could be a little opportunity for him to speak with the Deep. A Train is a tricky one for me. Pairing wise, I honestly ship Hancock with Maieve. They're both working to better themselves. Plus, it would be a good way for her to move on from Homelander. Speaking of Homelander, I can see Ryan looking up to Hancock instead of Homelander later on.