You don't really describe your current organization, so we cannot judge the ease at which you might do this by hand.
However, given that you have over 20K of images, "import from catalog" might be exactly what you want.
"Import from catalog" will move your edits into a new catalog.
"Include negative files" will copy your images into a new location and hierarchy.
Turn on the setting that says something like "use the import dialog" so that you can see/pick where things are going.
Run some tests with a small number of files to get a feel for what is going on and what options you need turned on.
This process will temporarily use 3x your current disk needs, so make sure you have enough room.
I'm curious why this effort to change your folders to capture date folders is even necessary. As ManiacJoe pointed out, you haven't described your current organization ... but ... you can find photos by capture date, right now, without you doing additional work. That capability is already present in your Lightroom catalog (assuming the photos were captured by a digital camera and not scanned). If you want to find your photos by capture date, the Filter Bar or a Smart Collection will do that right now, today, without you spending a large amount of effort setting it up.
Furthermore, it is always my recommendation that instead of putting effort into changing your photos into a capture date folder structure, you put your efforts into properly adding keywords and other metadata to your photo, this will give you a far superior organization than anything you could get via capture date organization.
DO NOT RE-IMPORT! You will lose some or all of your metadata. DO NOT RE-IMPORT!