What type of connector should I use for multichannel(16) RF analog signals? Can I use HDMI?
Get a shielded Ethernet cable:



This gives 4 shielded pairs, so just ground the white wire. You need 16 connections, so get 4 Ethernet cables. Voilla. 



EDIT

This appears to be more of what you need.




If I were you I would seriously just get some aluminum foil and wrap it around small cables and then put a heat shrink tube around the whole thing. (And ground the aluminum foils)