<font color='#000000'>OUCH! Jazz without sax is a hard task!
I'm not a real expert, but I can try to help. Be warned, though, you'll have to stand some sax playing in most of these, but not as the main focus.
Thelonious Monk would be a good start. He plays piano in a very unique way, but once you get used, you realize is really brilliant. "Brilliant Corners" is one of my fav.albuns of his. "Monk Alone" is a collection of his solo performances, if you want to avoid sax at all, but I find his band works more interesting.
Art Tatum is another great pianist. Very mellow, and great harmonies. I have "Tatum Group Masterpieces vol 8" and it's a incredible album.
John Pizzarelli plays guitar (no sax here!) in a kind of "retro" way. His father Bucky also plays guitar. I have his DVD-A "Swing Live". Very good album, with AMAZING sound, and no sax either.
Early George Benson albuns are great (before he started to sing). I have "Witchcraft", a live album with awsome music.
If you want to get more funky, You could go with Jimmy Smith (Hammond organ), Grant Green (guitar) or Lonnie Smith (also Hammond). This is as funky as it gets, but is a departure from more traditional jazz (call it jazz-funk if you want). Grant Green's "Alive", Jimmy Smith's "Back at the Chicken Shack" and "Home Cooking" and Lonnie Smith's "Live at Club Mozambique" are all good examples of this genre. Jimmy Smith doesn't use saxes, either.
About beeing made at the spot, it's not tottaly true. They improvise the solos (everyone has its turn), but the music itself is created and rehearsed before.
Hope this helps. Enjoy!
Fernando R. Kuhn</font>