Carrier Air V Lower Unit and other AC questions

Recently I was given a New, but out of the box, lower unit for my Carrier Air V RV AC. The unit did not have a remote control with it though. Would the remote for the presently installed Carrier Air V AC unit work on the new unit? Also, what type of wall mounted thermostat would be best to replace the older up and down slide type?
I'm in the process, while I have the energy, of remodeling the interior of my 04 Carriage Cameo.