I think it'd be a fun way to introduce Wolverine to the MCU but obviously the whole movie shouldn't be about their conflict. It's high time the Leader made his debut, so the main conflict should be around him.
Here's my pitch for this hypothetical Hulk solo movie: The Leader is aiming to put Gamma World into motion and he's made a ton of gamma mutants. Secretary Ross realizes the danger in this and remembers that Bruce was against Sterns experiments. As much as he hates the Hulk and puts up a public stance of military control over a "traitor" like Bruce, he knows he can't contain this threat on his own. He secretly asks Bruce for help. Bruce begrudgingly accepts.
Meanwhile, Xavier is also receiving word of a surge of mutations. He's obviously wanting Mutantkind to be received well when they finally reveal themselves to the public, but given the public reception to Inhumans he's made great efforts to keep secrecy (even using his telepathy to wipe the memories of anyone who knows of their existence). This gamma mutant problem (especially since the press are calling them mutants which is extremely problematic since that's going to confuse the public even more about the actual, X-Men related Mutants) threatens to delay their warm reception even further, so he sends an agent to address the threat and try to quell it...
The hotheaded Logan arrives on the scene in time to see Hulk fighting the gamma mutants. Logan has only recently been coaxed out of his decade long retreat to the Canadian wilderness (this version of him is even more of an outsider than Jackman's version and actually prefers isolation) so he's a bit behind on the happenings of the world. He doesn't really know who Hulk is so he treats Hulk as yet another target...
This Wolverine would be significantly stronger, faster and better trained than Jackman's. Much closer to his comic book counterpart than MCU Hulk even is to his counterpart, giving him a significant edge against the green goliath. He's got the savageness of Jackman's Wolverine but also the ninja training so he's able to do extremely swift and precise incisions to arteries and muscle groups that momentarily disable Hulk (but this is where we finally get on-screen demonstration of MCU Hulk having a regenerative factor). Ultimately though a front on assault proves futile since Hulk can just bat Wolverine miles away with a casual swing of the arm. Logan resorts to his stealth training.
By using the element of surprise he's able to latch onto Hulk's back. He pierces the nape of Hulk's neck, paralyzing him. Before he can finish Hulk off, the rest of Leader's forces advance, distracting Logan. Hulk's still conscious and pissed off beyond belief. His regenerative ability is quickly undoing the spinal damage...
Logan prepares for the oncoming horde of gamma freaks but before he can do anything, he's literally pummeled straight down into the ground by Hulk (like, picture the Wiley Coyote shaped hole in the wall thing, except down into the ground and more gruesome). His adamantium skeleton of course survives but his body is presumably wrecked with the gore conveniently concealed by the dust of the pummeling and the rubble burying him for that PG-13 rating.
Hulk is satisfied that his opponent is down and continues onto repelling the gamma mutants, his rage making it an easy clear and he then leaps away. Several hours later, Logan emerges from the rubble, recovers, and finally complies with Xavier's persistence that he continue his investigations despite all of Logan's complaining.
He finally finds Bruce (good news for Logan) and is eventually brought on board to help against the real threat. Sort of flipping the Ragnarok thing where Hulk is the unwilling helper to the protagonist's quest.