That's the way that I typically do a print screen.
I guess my question then is, do you really want different resolution or different clarity in the pasted image? If the latter, then what application are you using the pasted image for? The final viewing will depend on your printer if printed. Word changes the clarity even more if viewing electronically. Web page viewing will depend on the final users' settings.
I have found that the clarity on the screen is terrible because of the automatic scaling done by Editor. If I adjust the scale to 100%, the pasted image looks exactly like the original, assuming Editor is maximized.
Changing the resolution on the screen will only effect how much information is shown on the screen at any one time: i.e. icons are smaller and therefore more fit on screen, fonts are a little smaller, application windows show more of the data. A print screen dumps all that information to a temporay file (clipboard) that you then paste-as-new. If you really do mean change screen resolution, then you should be seeing more or less information on your print screen depending on your resolution settings. I would recommend the highest resolution of 1024 x 768 for your screen dumps (print screens) if used in another application because other users may only have a resolution up to 1024 x 768.
--Scott