OMFG, it just keeps getting worse.
This is what you will need to make this work (assuming this is a proper jamma cabinet and not a mame cabinet)
1 x capcom "Capcom vs street fighter" game board (these are called a B BOARD from now on)
1 x capcom motherboard (these are called an A BOARD from now on)
a whole mess of wires with a funny long plastic connector on one end (a JAMMA harnes)
a jamma cabinet with controls and a screen and a power supply.
OK, thats the easy bit, if you have all of this stuff you are well on your way.
First you get the B BOARD and plug it into the A board (no solder required)
Then you get the jamma harned and plug the funny long plastic connector into the sticky out bit on the A BOARD.
Then you get the otehr end of the JAMMA harnes, there should be a plug on the end for the Power supply and 2 x other plugs for the controlls. Plug them in and you chould be good to go. NOTE: sometimnes the other end of the jamma harness is already hard-wired onto the controlls and the power supply, if this is the case you won't need to connect them yourself.
Extra for experts: plug in the "kick harness" onto the B BOARD to get the other six buttons going.
So in answer to your question, you MIGHT be able to get away without soldering, it just depends on how your cabinet is set up (you DO have a cabinet, right?)