I am no expert, but I have hooked up at least 3 GPS receivers to NMEA devices successfuly, the last one was my Garmin chart plotter to a Standard Horizon radio.
Part of the problem is that GPS technology has advanced further than you need, and it may be hard to find a simple GPS "receiver only" that runs off 12 volts and sends a NMEA signal. I just spent half an hour googling and pretty much came up blank. Most of the interfaces from "receiver only" GPSs are either USB or Bluetooth, and not intended for a marine environment.
Here is one link that may help:
This one is NEMA 2000 compliant, Lowarance also makes a similar model that is NEMA 0183 compliant. My guess is (and this is only a guess) that you can cut the plug off the end of the cable leading from the GPS and wire it to 12v power and run 2 more wires to the NEMA input on your radio. I suspect that Garmin and Raymarine etc. offer similar GPS only products, I couldn't find one on Garmin's web site.
The Simplest and least expensive solution would be to buy a mount for your Garmin (if you havn't already), and a serial data/power cable with the bare wires:
Then drill some holes in the console to route the wires so that you can unplug the GPS and the radio when you are not around to watch them.
Hope this helps, l will be interested to hear how you solve your problem.