I would first consider whether you actually need real-time IK, or whether you can load your rig into an animation program such as Blender and design your animations ahead of time. Blender supports setting up constraints and IK for posing your model, which can aid you in making animations and poses which could then be exported to Panda3D. This will be sufficient if it is the case that all your animations (eg. walk, run, climb) are known ahead of time, such as in many games, but it will fall short if your models need to dynamically interact with the scene in complex ways (eg. a hand needs to reach out to touch an object at arbitrary location, or a foot needs to be precisely placed on an arbitrary obstacle). In those cases you may need IK.
Given that neither ODE nor Bullet actually support IK, I would not use either of them as a starting point for implementing IK unless I were already using those physics engines in my application.
There seems to have been an attempt to implement a FABRIK solver in Panda3D, but you would need to request them for the code.
It may also be that there are Python packages (such as this one) that can help you implement IK. You would mainly be writing the code that gets the joint information from Panda3D into the library, and get the transformed joints from the library back onto the Panda3D generated model.
Failing all that, I would suggest you look at an IK algorithm paper (such as FABRIK) and implement it on top of Panda3D directly. Let us know if you run into anything that you need help with; there are others on the forums here who are also interested in IK.