Doing this purely for battles is relatively straightforward.
What you want to do is, get yourself Luksy's ULGP tool; it's for unpacking model archives to be edited and then repacking them.
http://forums.qhimm.com/index.php?topic=12831.0Go to the FF7/DATA/BATTLE folder and grab the battle.lgp archive from it. Unpack it using ULGP and it should give you a folder with all the loose model files inside. The model files/parts are identified by the first two letters in the file name, so everything starting with 'RT' for instance belongs to Cloud's model.
RTAA: Cloud
RUAA: Tifa
RVAA: Aeris
RWAA: Red XIII
RXAA: Yuffie
RYAA: Cait Sith
RZAA: Cid
SAAA: Sephiroth
SBAA: Barret A
SCAA: Barret B
SDAA: Barret C
SEAA: Barret D
SFAA: Vincent A
SGAA: Vincent B
SHAA: Vincent C
SIAA: Hi-poly Cloud
As a sidenote, there are multiple copies of Barret and Vincent to handle different weapon animations in case you're wondering.
So what you can do here is, you can make a copy of Sephiroth's 'SA' files and then rename them to match a different character's files. When the game loads that character, it'll have Sephiroth's battle model instead.
If we delete all of, for example, Yuffie's files (any file starting with RX) and then rename our copied Seph files to use RX instead of SA, then whenever Yuffie is in a battle it'll load Sephiroth's battle model.
For the weapons, we can get away with just replacing the first weapon with Sephiroth's only weapon but for more variety you could grab Cloud's weapon files and use those to replace the remaining weapons; weapon files typically always have a 'c' as their 3rd character; so all 'RTC' files are all Cloud's weapons, 'RXC' are all Yuffie's weapons, etc.
When finished, repack the archive and put it back into the ff7/data/battle folder.
For the menu portraits, you want to head into FF7/DATA/MENU and extract the menu_us.lgp. In here you'll find a bunch of .TEX files that handle character portraits in menus + smaller versions for PHS/shop menus. Same deal here; get rid of the target character's files and replace them with a renamed copy of Sephiroth's files.
For the weapons + stats, you'll want to use the kernel editor 'Wall Market' (install Visual Basic Power Pack 3 to get this tool working on newer machines).
If you pop open the kernel.bin (located in ff7/data/kernel for old FF7 PC, and in ff7/data/lang-en/kernel for steam version) you'll be able to modify your target replacement character's starting weapons, stats, etc. for something closer to what you'd expect Sephiroth to have. You can rename the weapons too if you want.
As for field screens, that's a bit more involved as there are a lot of screens, animations, etc. to change (and dialogue, assuming). You might be best leaving this as-is unless you want to undertake your own project to changing it all.