Umm... Go buy an SiR. There's your splice-free part.
Here's the issue: Your CRX originally had its VSS (vehicle speed sensor) attached to the back of the cable-driven speedometer. Your new speedometer relies on the pulsing VSS signal to determine speed, rather than a spinning cable. Since you got rid of the stock gauge cluster, the car no longer has a VSS. No VSS means no VSS signal, and your new speedo has no way of knowing how fast the car is moving.
Thankfully, all '92+ Civics switched over to the electronic speedo system that the SiR uses. That means you can take the transmission-mounted VSS from a newer Civic and bolt it to your transmission in place of the cable drive gear assembly... The parts that actually connect to the transmission are the same size as the stock drive gear, so the newer VSS unit just drops in. '92-95 Civic units are a good bit more bulky than '96-05 Civic sensors, enough so that they can run into the engine mount, requiring that you cut chunks of material off the sensor to make it fit. The later, more compact sensors just drop in in my experience.
If you're not willing to connect the new sensor to power, ground (both found in the engine harness) and your existing VSS wiring (gotta run a wire through the firewall), you're SOL - To my knowledge, nobody makes a plug-in harness to convert to a transmission-mounted VSS.