Not a chemistry answer: but a very successful one, in my experience: get a Ropump. It's a cross between a plunger and a bicycle pump. It makes drain-unclogging a pleasure.
Mechanical action is just so much more successful for this task, than chemical. Because water is extremely resistant to being compressed, the Ropump's action, in turning water into a liquid drain rod and forcing it down the drain, has a pretty high success rate.
You pull plunger out, while the far end sits in a reservoir of water. This fills the body of the pump with water. You then fit the far end over the blocked drain, and push the plunger in, forcing the water down the drain, and displacing the blockage.
In the end, you don't know what the chemistry is at the blockage. So it's easier to anticipate the unintended consequences of a mechanical, rather than chemical, intervention.