If you wish to produce a final result that has the HDR look you get by doing a 5 exposure bracket and also demonstrates the blurred water you get by doing a 20 image stack then you need to produce multiple series of your 20 image stack.
Do a 20 image series at -2. Do another 20 image series at -1. Do a 20 image series at 0, another 20 image series at +1, and finally a 20 image series at +2. That way each of your source images includes the blurred water.
Once you've done that you can then stack each series of 20 images independently to create 5 stacked images: one each at -2, -1, 0, +1, and +2. You would then import those five images into your HDR software to produce your final image.
For best results convert each of your 100 raw image files into a 16-bit TIFF to use in the stacking process, then export the results of each of those stacks as 16-bit TIFFs to import into your HDR application. You'll need massive amounts of processing power and large amounts of RAM memory (if your applications can even handle such large files) as well as plenty of storage space on your hard drive. Still be prepared to wait a while as your computer does each of the necessary processing steps.
Or you could just cave and use an ND filter. A four-stop filter would allow you to extend the exposure time by a factor of 16 so your results with one exposure would be very close to your 20 shot stack. A 2-stop and 4-stop filter could be combined to give a 2, 4, and 6-stop ND reduction series (using both filters together for the 6-stop exposure) using the same shutter time and aperture value. There's your -2, 0, +2 series needed to do an 5-stop HDR. In only three clicks of the shutter, rather than 100.
There's a reason that the top landscape photographers in the digital age still use filters in front of their lenses for many of the photos they produce. Even if the same thing might be done using digital post processing techniques there is usually a price to be paid. That price may be in terms of the ultimate quality of the final image. That price may be in terms of the hours of time needed to do with software what can be done in mere seconds in-camera. Often it is both.
Imagine the amount of time that would be needed to edit reflections out of scene that could have easily been avoided by placing a polarizing filter in front of the lens when the image was shot! Even after all of that editing there will be artifacts left behind by the editing process that can't be removed. The same is true of stacking multiple images. We do so when there are no better options such as with the minute amounts of light collected by the widest lenses in astrophotography. The same is true of multiple-frame HDR techniques when the dynamic range of a scene exceeds the limits of our camera and our display methods.
The entire reason we do HDR Imaging of a high dynamic range scene with multiple frames taken at varying exposure levels is to avoid the negative consequences of trying to pull the highlights while also pushing the shadows from a single raw file. The reason we use polarizing filters is to reduce reflections or to increase contrast and saturation without adding the quality sacrificing artifacts of doing so in post processing. The reason we use ND filters is to reduce the amount of light striking the sensor for a specific amount of time that would otherwise result in a solid white photo.