I did like those 3D-print models that guy made.
http://forums.qhimm.com/index.php?topic=4194.0That's the Kimera tool thread; it's to be used with the PC assets (doesn't work with the PS1 models) but they're visually identical anyway; if they appear different in-game it's because of the resolution, renderer, etc.
You'll need to decompile the .lgp archive where the models are stored. The battle models are stored in battle.lgp, field models in char.lgp. To decompile them, use Luksy's ULGP tool. Once they're decompiled, you can open a char.lgp model with it's master file (.hrc). Cloud's is AAAA.hrc for instance.
In the battle models, they don't seem to have extentions but the last two letters of the file name denote what kind of file it is. 'AA's are the master file, so opening RTAA will open Cloud's model, etc. I don't know how to get them into another program from there, but hopefully that helps with the first step. And this'll help:
https://docs.google.com/spreadsheets/d/1OnCCU0OfV4khZ5eDOyBv-TADnWmvxGnqM3BV-KRqf7g/pub?gid=4