What you need to do is some pixel aspect ratio correction.
I need to change the image aspect ratio without changing the pixel dimensions.
Actually you do need to change the pixel dimensions. Or the pixel dimensions of the content of your image (meaning some of it will be cropped). Your image is being stretched as it is now, so the dimensions of something need to change.
In Photoshop you can set the view to compensate for various pixel aspect ratios. With a document open, choose View → Pixel Aspect Ratio and then choose a pixel aspect ratio that’s compatible with the video format that you’ll be using.
There are a number of predefined aspect ratios or you can set your own custom value. More about pixel aspect ratios in Photoshop here: Photoshop Help / Adjust pixel aspect ratio
Setting the the Pixel Aspect Ratio in this manner only changes the view for preview purposes—It doesn't actually affect your file in any way. What you need to do is correct your file so that it appears correct in your desired pixel aspect ratio.
You can either do this by-eye and adjust untill you are happy with the result—Or, since you know the ratio, stretch the image by that amount.