You will need to interpolate the values in the image position patient (
https://dicom.innolitics.com/ciods/ct-image/image-plane/00200032 )
If the CT is "perfectly lined up on the Z axis" then you need to get the 3rd value in image position patient and interpolate between the adjacent original CT.
It's certainly possible. It would be very time consuming to do it manually.
Doing it programatically is entirely possible. packages like pydicom can be used in python scripts and the amount of code involved is under 100 lines of code for the simple case.
You might not get what you are hoping for though.
If you have large gaps between slices (e.g. spaced by 3 cm, but each CT was actually only 1mm thick), it won't change what it looks like, it will be a sharp transition every Nth slice still. If the slices are just very thick (e.g. 1cm thick, and space by 1 cm), then it will be just as chunky.
If what your situation is calling for is that your voxels need to be isotropic (the thickness is the same as the pixel size in a single slice), then you have to "re-slice" your volume, and the hack you mention isn't going to do the job.
Best of luck (sorry, I'm overwhelmed with my day job to moonlight...)