My thought was that if Cormier beat Mir he'd probably stay HW. If he lost to Mir then he'd drop and possibly take on Jones somewhere down the line.
I don't think Cormier is staying at HW either way as long as Cain has the belt. He'll at least try to drop down to LHW rather than have to choose between fighting Cain or giving up trying to get a title.
Cormier will open at probably about a 2-1 favorite over Mir. Mir is my favorite fighter, but stylistically Cormier is a tough matchup. I think the boys at AKA will be happy to have Cormier keep the fight standing with Mir. Mir's striking is a bit more polished overall, but Cormier has naturally better hands and seems to recover better from getting hit.
If Cormier takes the fight to the ground, he's playing with fire. Cormier has tremendous top control but his gnp is only okay at this point and his submission game from the top in nonexistant. He also leaves limbs out there fairly recklessly which is asking for trouble against a guy who's so aggressive looking for subs from the bottom. (People want to point to the Barnett fight as an example of Cormier's sub defense, but Josh is way more aggressive with his subs from the top than he is from guard. I don't think Barnett and Mir are all that similar stylistically as submission fighters, though both are terrific at HW in subbing guys).
Cormier said he wants Jon Jones in the fall. I really wonder about him fighting at HW in April and then cutting to 205 within 6 months given his previous health issues. Maybe he does it no problem, maybe not. Either way, I think Jones is a horrible matchup for Cormier at LHW. Even if the weight cut doesn't drain Cormier too badly, he's going to eat a lot of shots trying to get in close to Jones. And while he can probably walk through them to a degree, they will accumulate and take their toll. And then he's in close with a guy who's clinch game and ability to use leverage has blossomed into truly elite status over the last few years. Cormier's olympic wrestling pedigree is obviously impressive, but Jones (like GSP) has grown his wrestling game to the point where he ragdolls everyone he fights, including guys with far superior wrestling pedigrees. I'd be pretty surprised if Cormier beat Jones at LHW. I'd give Cormier a moderately better chance at a catchweight fight of say, 220.