The BU-353 will not work, but the BR-355 or MR-350P are Serial GPS Receivers that are more appropriate for that type of usage. You would have to check that your Cobra VHF radio uses the NMEA protocol. If so, then technically it should work. However, we cannot guarantee that it will work as we have not tested it.
Here are the pin outs (http://www.usglobalsat.com/store/download/58/mr350p_ds_ug.pdf
1 - Black - Ground
2 - Red - VCC - 5V input
3 - N/A
4 - White - RX - Receive - connects to NMEA out
5 - Green - TX - Transmit - connects to NMEA IN
6 - N/A
With this information, you should be able to set it up. If you need additional help, I would suggest contacting the manufacturer of the VHF radio.