You can have FBX files with no meshes in and import only the animation if the FBX contain everything that is animated (the skeleton if you animated the bones only and the meshes if you have morph animation, of course)
But for your imported animation to works with a skeleton in UE4, they must have the same bone hierarchy. You can use the retargetiong tools to make an animation work with another skeleton but you will have to keep some similarity between the two skeletons.
It depends of the bones hierarchy.
Even if the bones doesn’t have the same names in both skeleton, you can use the humanoid rig to match your skeleton with the SK_mannequin… But you need to know if the bones are arranged between them in the same way the SK_mannequin is.
Did you tried to select the SK_mannequin skeleton while an import ? Maybe it will work.
If not, you’re not screwed… You’ll need to retarget your animation for the skeleton you want to use with them.
I think that the MoCap software is meant to do this but I don’t know it for sure.
You should open your FBX file with any software to see how the bones are attached to themself.
Eventually, add a simple mesh and skin it to some bones. Then, import the new FBX (with a mesh) in UE4. Make the retargeting from your skeleton to the UE one. You will be able to import the other animations on the skeleton you retarget to.