In Photoshop, make a copy of your main layer. Call it, say, "Darken".
(Optional) Use a layer mask for the copied layer to mask out the main object, like a galaxy or nebula. This will leave just the stars that are trailing visible on that layer. (You can try it without this step, but often the effect on the main object is too severe). To do this, I will frequently select "white" for the foreground color, then 'select/color range' to pick up just the stars in the photo. I will expand the selection by 4 pixels, the feather by 2. This ensures that only the stars in the photo will be adjusted.
Change the blend mode of the "Darken" layer to "darken". The theory is that wherever a pixel in this layer overlaps the main layer, the program will choose the darker of the two pixels to display.
So... now click on the "Move Tool" in the toolbox.
Make sure the image section of the copied layer ("Darken") is selected - click on it. You don't want another layer, or the layer mask of the copied layer to be selected.
Use your cursor keys to 'nudge' the copied layer around - you will be overlaying the darker pixels of the copied layer so that they eliminate the trailed sections of the stars!
Use your cursor keys to 'nudge' the copied layer around - you will be overlaying the darker pixels of the copied layer so that they eliminate the trailed sections of the stars! You want to get within one pixel accuracy in both directions.
If You Need More Adjustment Accuracy:
Instead of just using the cursor keys to nudge things around, use the "Filter/Other/Offset" command to move that "Darken" layer for that final portion-of-pixel differential. Now, use the "Edit/Fade Offset" command to finely adjust the amount by which the filter is applied. (I generally do one axis at a time.) This gives you the appearance of extremely precise pixel control. (In actual fact, the before and after states are blended to produce your final results.) Therefore, don't use this method except for the portion of the final pixel.
Alternatively, you can upsize your document 400-500% before nudging the layer around. In this example, it gives you 1/4 or 1/5th of a pixel accuracy once you resize back to the original size.