Replacing the thermostat should not require re-gassing the system. It is totally unrelated, save from the electrical system (thermostat) sending signals to the gas system through an interface. That is, a signal from the thermostat tells the gas system the fridge/freezer is too warm, start working. It does this by tripping a switch which sends a signal to the compressor. The compressor then starts working, cooling the interior. I have probably not explained this too well, but I hope you get the gist. Everything else being equal, if the thermostat needs replacing, and you have the necessary skills, replace it and all should be well. If you have any doubts, and your request suggests you may have, then have it done by a qualified engineer.
Paul Higgins, July 2005