Baseline (Widescreen) Solution & Issues
To add widescreen support to this game you'll need a hex editor such as Be.HexEditor. Open your Skate3.exe file and search for the line 0000b400 or search for the string highlighted below (and make sure it's on that line).
The groups 80 02 and e0 01 represent the resolution 640x480. What we'll do is change them to represent the widescreen resolution we want.
1280x720 - Replace 80 02 with 00 05 and replace e0 01 with D0 02
1280x800 - Replace 80 02 with 00 05 and replace e0 01 with 20 03
1366x768 - Replace 80 02 with 56 05 and replace e0 01 with 00 03
1440x900 - Replace 80 02 with A0 05 and replace e0 01 with 84 03
1680x1050 - Replace 80 02 with 90 06 and replace e0 01 with 1A 04
1920x1080 - Replace 80 02 with 80 07 and replace e0 01 with 38 04
1920x1200 - Replace 80 02 with 80 07 and replace e0 01 with B0 04
Once you're done, save the file and make sure you have 640x480 selected in the THPS3Setup.exe program.
I didn't notice any problems in 1440x900, but unfortunately the game just stretches, as you can see.
Ultra/Super-Wide (21:9/32:9) Specific Solution & Issues
Eyefinity / Surround Specific Solution & Issues
4k UHD Specific Solution & Issues