Yeah the controller is an equivalent of the T6963C which were ubiquitous for those displays. To make it "controllerless" you do indeed only need to remove the controller and SRAM. ]
It might also have built-in DC-DC converter for the -VEE required by the display (about.. -12V I think..) that should be enabled after the control signals - if your new controller board provides this you will need to modify this part as well.
I am assuming the control signals your new board provides are the semi-standard FR/CP1, LP/C2, DATA, S, M etc.. but off the top of my head.. I think these signals are different from the 4-bit interface of larger panels, so only 5 signals required. If you compare the original LCD's datasheet to the RA6963, then it looks like...:
orginal LCD - RA6963 name - pin number
CP1 - LP - 55
CP2 - SCP - 53
S - FLM - 59
M - M (FR) - 57
DI - D1 - 56
I could be wrong here!
So yeah, looks like a bit of an arse to map out pins - especially as the original t6963C was a joke, and the newer RA6963 ain't much better in terms of pin names (they happily use LP and CP1 interchangeably) it certainly can be done. My only additional advice would be to check the outputs from the original board on a logic analyser to double check that the signals are what you think they are.
Otherwise you'll have to use the original LCD's datasheet pinout to find the signals on the original board.. and the RA6963's datasheet to find the corresponding pads on the RA6963s footprint on the new LCD, whilst you can keep track of that, there's a lot of room for error. With that said I can't see you permanently destroying anything - except perhaps the outputs of the original boards if they were shorted to ground, but a quick continuity check will prevent that.
Ok so my only advice would be... use a pin header and socket and decide on your own pinout, so that when you mod the new LCD you know the exact pinout of your connector, and the same with the old board. That may sound obvious, but when patching wires directly it can become a mess very quickly, and you can lose track of what signals are what.