Photoshop :: Crop Tool Re-crop By "ratio"

I've been using the crop tool without any knowledge of the little boxes you can fill in to restrict its WxH dimensions. I always wanted my crops to come out at a 2:3 ratio and could never get them perfect since I was just eyeballing it.

So then I found the WxH controls and if I put "2 in" for width and "3 in" for height, my image will come out as desired, no scaling of the image, but with the unfortunate side effect that my DPI has been changed, which causes problems for me later on. Now if I put "2 in" x "3 in" and then specify 72dpi in the "resolution" field, it will actually scale my image which is not what I want either. Now if I put "2 px" by "3 px" of course it will massively scale my image, which again is not what I want.

What I want is to re-crop my image to a 2:3 ratio, WITHOUT scaling, AND without modifying DPI. Is this possible with the crop tool? It seems that my WxH numbers are required to have units after them and I don't want any of those units (inches, px, mm, etc). I want unitless cropping, basically cropping by ratio. Does this make any sense?

I have a work-around which involves batch resetting all my DPI's at the end of the session. But that adds another step to my workflow which is not a very elegant solution.