That's no problem. I have a widescreen with 1920x1480 and I run SH3 at 1600x1200 fullscreen with no problems. (I probably could run it in 1800x1350, which would also be 4:3, I have to try that).
To do that, you either have to use the graphic card settings to force any application changing resolution to keep the aspect ration (better 3d cards have that). Also the monitor might have a hardware setting for that (via the menu).
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