Noting further that this still works with the SYW Mods, since after installations are done, it still uses the base "ff7.exe".
Funny that I went looking for this info in Google, because I knew I'd seen it before, but didn't remember that I was the one who shared the info on here to begin with!

I realised that my own instructions were a bit... Unclear.
I've made my changes using the Hex-editing program "HxD". If you're using it, go to the "Search" menu, then "Go to", and put
236a7din the "Offset:" box, with "hex" selected underneath it.
That will put the cursor at a section that says "D2744D0F"
Change only that "74" to "75" (it will turn the numbers red to show they've been changed); that section should now show "D2754D0F".
Go back to Search then "Go to", and put this in the Offset box:
233d92You'll be in a section that says "85C97454".
Change only the "74" to "75". That section should now say "85C97554".
You've done both the necessary changes, so just go to File, then Save.
Load up the game, and you'll find that running is now the default, with the Cancel button being used to walk instead.
Done!