Legends of Wrestling (2001) and Legends of Wrestling II (2002) on PS2 have no online sharing, no community servers, and no built-in CAW export/import. Memory cards (8 MB) store CAWs locally only.
If deep creation/sharing matters, play WWE SmackDown! Here Comes the Pain (PS2) or WWE 2K22/2K23/2K24 (PS4/5, Xbox, PC) — Community Creations servers host 100,000+ downloadable CAWs with images, tags, ratings.
Legal: Downloading save files is generally fine for personal use; distributing copyrighted likenesses (real wrestlers) in CAWs is a gray area.