It is possible to import some existing Skyrim animations to edit them with Cascadeur.
First, you have to import your hkx animation into Blender using the same plugin we usually use to export. It only supports the import of animations from 32-bit Skyrim LE, so you’re going to need that to proceed. If you can’t easily procure an LE variant and need to convert an existing 64-bit SE hkx to LE, you can read about that at the bottom (it takes a few minutes).
Using an empty new scene in Blender, go to File – Import – Havok Animation (.hkx) in Blender, pick your animation, make sure the correct skeleton is selected, and the Scale is set to 1.
If everything goes well, and a non-descript pile of dots loads, go to File – Export – FBX. Pick a scale of 0.01 in the FBX export menu.
Open Cascadeur and create a new empty scene. Drag and drop the new FBX file there. Nothing will show up, but you can notice a new object in the outliner. Switch to Joint mode, and you’ll see the outline of Skyrim’s imported skeleton with the animation we’ve just imported.
Pay attention to its length at the bottom, where the timescale is located. Select the whole interval. Select all of the diamond-shaped markers with the right mouse button. Click Edit -> Copy Interval in the top menu.
Good news - we’re more than halfway there. Now let’s import the animation to the rig. Open the rig file and extend the length to match the one in the imported animation. Select the entire length of the timescale. Switch to Joint mode and select the same diamonds in the rig. Click Edit -> Paste Interval and it should copy the animation from the FBX to the rig.
Spoiler: 
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Now, in order for it to be easily editable, you’re going to need to reduce the keyframes, so the edits interpolate well. The import process is going to copy each and every keyframe, and unless you want to tediously edit each keyframe (not recommended), you should really try to leave only the main keyframes where something happens.
Users of Cascadeur version 2024 and up can take advantage of the automatic animation unbaking tool - but as with any automatic tool, it can produce rather mixed results at times. 2023 users can try using this keyframe reduction add-on from here . Mass-deleting keyframes manually can be done by selecting an interval and pressing Alt-F.
Pick the interpolation mode between keyframes - and edit the ones that you left, add new ones, or perform edits across all keyframes with the special mode, etc.
--- part where you draw the rest of the @#$! owl happens here ---
Afterwards, just export it back to Skyrim via usual measures and try it out!
Converting animations from SE to LE
This can be achieved using the Standalone Filter Manager from the Havok Content Tools suite. It’s a bit tough to get nowadays, but I’ve heard that googling something like “HavokPcXsContentTools_X64_2010-2-0_20101115” might set you on the right track. ;-)
Load your animation with it (Open – Done – OK), pick Write to Platform in the left pane, add it to the right pane, pick a name, and select Format: Packfile – Win32MSVC. Click the “Run all configurations” button at the bottom.
Collect your 32-bit LE hkx from the folder and feed it to the plugin.
Video materials:
Skip to 3 minutes in, and you'll be able to see the same process I've outlined here.
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[EDIT] Thanks @krzp1 for pointing me to the pre-built version: https://www.nexusmods.com/skyrimspecialedition/mods/118525?tab=description