3. paste the capture into PhotoShop
4. Transform/Scale the image from it's captured size (760 pixels x 550 pixels) down to a 165 x 115 pixel thumbnail
First, don't use transform/scale. Use the Image...Image Size command. It should already be set correctly to 72 dpi, constrain dimensions (checked), resample...bicubic (checked). If not, make it so.
Now, resize in steps. If you're starting with 760, half it. Now resize again at least once more. I'd probably divide the max dimension into three or four and resize it progressively down.
Next apply an Unsharp Mask (Filter...Sharpen...Unsharp Mask). Somewhere between 50 and 100% should do the trick. Every once in awhile there is value to sharpening after each resize. It depends on the image. You could also use bicubic sharpen but honestly I usually see better results with a sharpen only applied on the final image.
Alternately, if you're trying to include thumbnails of screenshots in a print portfolio (?), go to Image...Image Size and change the resolution to 300. Keep the constrain dimensions checked, but this time change the resample dropdown to "Nearest Neighbor" (checked). This last part will avoid anti-aliasing. Key is saving it as a TIF or similar at this point...If you "save for web..." you'll end up back at 72 dpi.