First of all, I'd suggest to not change this at all, because of some issues you might get there. I'd suggest to migrate all the images that you have in your media/ folder to media/wysiwyg/. And also check the image paths that are now broken in your database.
But if you really want to change it, there is a model "Mage_Cms_Model_Wysiwyg_Config" where the constant "IMAGE_DIRECTORY" is set. This is set to "wysiwyg". So it might be possible to create a custom extension/addon for this, where you can override this constant. Changing it with an empty string might work.
I haven't tested this myself, because I don't think it's a proper solution, so it might not work in the end or give you a lot of issues and errors.
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